arXiv subjects

Claudia Ceci

Publications and source records attributed to Claudia Ceci.

At least 19 recordsLinked to original sources

arXiv2026

Filtering in a hazard rate change-point model with financial and life-insurance applications

This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a firm or the mortality rate of an individual may experience a sudden jump at an unobservable time, representing, for instance, a shift in the firm's risk profile or a deterioration in an individual's health status. By employing a progressive enlargement of filtration, we integrate noisy observations of the hazard rate with default-related information. We characterise the filter, i.e. the conditional probability of the change-point given the information flow, as the unique strong solution to a stochastic differential equation driven by the innovation process enriched with the discontinuous component. A sensitivity analysis and a comparison of the filter's behaviour under various information structures are provided. Our framework further allows for the derivation of an explicit formula for the survival probability conditional on partial information. This result applies to the pricing of credit-sensitive financial instruments such as defaultable bonds, credit default swaps, and life insurance contracts. Finally, a numerical analysis illustrates how partial information leads to delayed adjustments in the estimation of the hazard rate and consequently to mispricing of credit-sensitive instruments when compared to a full-information setting.

q-fin.MF↗

arXiv2025

Explicit Solution to a government debt reduction problem: a stochastic control approach

We analyze the problem of optimal reduction of the debt-to-GDP ratio in a stochastic control setting. The debt-to-GDP dynamics are modeled through a stochastic differential equation in which fiscal policy simultaneously affects both debt accumulation and GDP growth. A key feature of the framework is the introduction of a cost functional that captures the disutility of fiscal surpluses and the perceived benefit of fiscal deficits, thus incorporating the macroeconomic trade-off between tighten and expansionary policies. By applying the Hamilton-Jacobi-Bellman approach, we provide explicit solutions in the case of linear GDP response to the fiscal policies. We rigorously analyze threshold-type fiscal strategies in the case of linear impact of the fiscal policy and provide closed-form solutions for the associated value function in relevant regimes. A sensitivity analysis is conducted by varying key model parameters, confirming the robustness of our theoretical findings. The application to debt reduction highlights how fiscal costs and benefits influence optimal interventions, offering valuable insights into sustainable public debt management under uncertainty.

econ.GN↗

arXiv2025

Self-protection and self-insurance for general risk models via a BSDE approach

We investigate an optimal prevention and insurance problem in a general risk setting, where a representative agent is exposed to potential losses. The agent adopts a strategy that combines self-protection, aimed at reducing the frequency of claims, and self-insurance, aimed at mitigating their severity. The problem, which consists in maximizing the expected exponential utility of terminal wealth, is formulated as a stochastic control problem and solved by means of backward stochastic differential equations (BSDEs). Our approach, essentially based on a general Bellman Optimality Principle (see [13] among others), does not require specification of the underlying filtration structure, making it applicable to a broad class of risk models, including Markov-modulated, stochastic factor, Cox-shot noise and self-excited models. We extend recent results by [3, 5], which focused on self-protection in specific models, by allowing for both self-protection and self-insurance within a unified and general framework.

math.OC↗

arXiv2024

Optimal reinsurance in a dynamic contagion model: comparing self-exciting and externally-exciting risks

We investigate the optimal reinsurance problem in a risk model with jump clustering features. This modeling framework is inspired by the concept initially proposed in Dassios and Zhao (2011), combining Hawkes and Cox processes with shot noise intensity models. Specifically, these processes describe self-exciting and externally excited jumps in the claim arrival intensity, respectively. The insurer aims to maximize the expected exponential utility of terminal wealth for general reinsurance contracts and reinsurance premiums. We discuss two different methodologies: the classical stochastic control approach based on the Hamilton-Jacobi-Bellman (HJB) equation and a backward stochastic differential equation (BSDE) approach. In a Markovian setting, differently from the classical HJB-approach, the BSDE method enables us to solve the problem without imposing any requirements for regularity on the associated value function. We provide a Verification Theorem in terms of a suitable BSDE driven by a two-dimensional marked point process and we prove an existence result relaying on the theory developed in Papapantoleon et al. (2018) for stochastic Lipschitz generators. After discussing the optimal strategy for general reinsurance contracts and reinsurance premiums, we provide more explicit results in some relevant cases. Finally, we provide comparison results that highlight the heightened risk stemming from the self-exciting component in contrast to the externally-excited counterpart and discuss the the monotonicity property of the value function.

math.OC↗

arXiv2024

Portfolio and reinsurance optimization under unknown market price of risk

We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control problem under the observation filtration only, the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton-Jacobi-Bellman equation, and to provide explicit formulas for the value function and the optimal investment-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments.

q-fin.PM↗

arXiv2023

Optimal reinsurance via BSDEs in a partially observable model with jump clusters

We investigate the optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximize expected exponential utility of terminal wealth and show that an optimal solution exists. By exploiting both the Kushner-Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterize the solution of the stochastic optimization problem in terms of a BSDE, for which we prove existence and uniqueness of solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases.

math.PR↗

arXiv2021

A Stochastic Control Approach to Public Debt Management

We discuss a class of debt management problems in a stochastic environment model. We propose a model for the debt-to-GDP (Gross Domestic Product) ratio where the government interventions via fiscal policies affect the public debt and the GDP growth rate at the same time. We allow for stochastic interest rate and possible correlation with the GDP growth rate through the dependence of both the processes (interest rate and GDP growth rate) on a stochastic factor which may represent any relevant macroeconomic variable, such as the state of economy. We tackle the problem of a government whose goal is to determine the fiscal policy in order to minimize a general functional cost. We prove that the value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation and provide a Verification Theorem based on classical solutions. We investigate the form of the candidate optimal fiscal policy in many cases of interest, providing interesting policy insights. Finally, we discuss two applications to the debt reduction problem and debt smoothing, providing explicit expressions of the value function and the optimal policy in some special cases.

econ.GN↗

arXiv2021

Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets

We study optimal proportional reinsurance and investment strategies for an insurance company which experiences both ordinary and catastrophic claims and wishes to maximize the expected exponential utility of its terminal wealth. We propose a model where the insurance framework is affected by environmental factors, and aggregate claims and stock prices are subject to common shocks, i.e. drastic events such as earthquakes, extreme weather conditions, or even pandemics, that have an immediate impact on the financial market and simultaneously induce insurance claims. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we provide a verification result for the value function via classical solutions to two backward partial differential equations and characterize the optimal reinsurance and investment strategies. Finally, we make a comparison analysis to discuss the effect of common shock dependence.

q-fin.PM↗

arXiv2021

Optimal reinsurance problem under fixed cost and exponential preferences

We investigate an optimal reinsurance problem for an insurance company facing a constant fixed cost when the reinsurance contract is signed. The insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level in order to maximize the expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér-Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations.

q-fin.MF↗

arXiv2020

Indifference pricing of pure endowments via BSDEs under partial information

In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the so-called indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the indifference price of the insurance derivative via the solutions of suitable backward stochastic differential equations.

q-fin.MF↗

arXiv2020

A BSDE-based approach for the optimal reinsurance problem under partial information

We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.

q-fin.MF↗

arXiv2019

Value adjustments and dynamic hedging of reinsurance counterparty risk

Reinsurance counterparty credit risk (RCCR) is the risk of a loss arising from the fact that a reinsurance company is unable to fulfill her contractual obligations towards the ceding insurer. RCCR is an important risk category for insurance companies which, so far, has been addressed mostly via qualitative approaches. In this paper we therefore study value adjustments and dynamic hedging for RCCR. We propose a novel model that accounts for contagion effects between the default of the reinsurer and the price of the reinsurance contract. We characterize the value adjustment in a reinsurance contract via a partial integro-differential equation (PIDE) and derive the hedging strategies using a quadratic method. The paper closes with a simulation study which shows that dynamic hedging strategies have the potential to significantly reduce RCCR.

q-fin.RM↗

arXiv2019

Optimal excess-of-loss reinsurance for stochastic factor risk models

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate $r$. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.

q-fin.MF↗

arXiv2019

Optimal Reduction of Public Debt under Partial Observation of the Economic Growth

We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government's criterion is to minimize the sum of the total expected costs of holding debt and of debt's reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. These are described through a finite-state continuous-time Markov chain. We reduce via filtering techniques the original problem to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialize to a case study in which the economy faces only two regimes, and the macroeconomic indicator has a suitable diffusive dynamics. In this setting we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

math.OC↗

arXiv2018

Optimal proportional reinsurance and investment for stochastic factor models

In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend the classical Cramer-Lundberg model introducing a stochastic factor which affects the intensity of the claims arrival process, described by a Cox process, as well as the insurance and reinsurance premia. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation we characterize the optimal strategy and provide a verification result for the value function via classical solutions of two backward partial differential equations. Existence and uniqueness of these solutions are discussed. Results under various premium calculation principles are illustrated and a new premium calculation rule is proposed in order to get more realistic strategies and to better fit our stochastic factor model. Finally, numerical simulations are performed to obtain sensitivity analyses.

q-fin.RM↗

arXiv2017

Risk-Minimizing Hedging of Counterparty Risk

We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using the Galtchouk-Kunita-Watanabe decomposition of the counterparty risk price payment stream, we recover a closed-form representation for the risk minimizing strategy in terms of classical solutions to nonlinear recursive systems of Cauchy problems. We discuss applications of our framework to the most prominent class of credit derivatives, including credit swap and risky bond portfolios, as well as first-to-default claims.

q-fin.RM↗

arXiv2016

Unit-linked life insurance policies: optimal hedging in partially observable market models

In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering.

q-fin.MF↗

arXiv2016

The Föllmer-Schweizer decomposition under incomplete information

In this paper we study the Föllmer-Schweizer decomposition of a square integrable random variable $ξ$ with respect to a given semimartingale $S$ under restricted information. Thanks to the relationship between this decomposition and that of the projection of $ξ$ with respect to the given information flow, we characterize the integrand appearing in the Föllmer-Schweizer decomposition under partial information in the general case where $ξ$ is not necessarily adapted to the available information level. For partially observable Markovian models where the dynamics of $S$ depends on an unobservable stochastic factor $X$, we show how to compute the decomposition by means of filtering problems involving functions defined on an infinite-dimensional space. Moreover, in the case of a partially observed jump-diffusion model where $X$ is described by a pure jump process taking values in a finite dimensional space, we compute explicitly the integrand in the Föllmer-Schweizer decomposition by working with finite dimensional filters.

math.PR↗