arXiv subjects

Rafael Serrano

Publications and source records attributed to Rafael Serrano.

10 recordsLinked to original sources

arXiv2023

Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

We study investment and insurance demand decisions for an agent in a theoretical continuous-time expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a jump-diffusion process with negative jumps in the return rate of the (self-financed) wealth. The main distinctive feature of our model is that the agent's decision on portfolio choice and insurance demand causes nonlinear friction in the dynamics of the wealth process. We use the dynamic programming approach to find optimality conditions under which the agent assumes the insurable risk entirely, or partially, or purchases total insurance against it. In particular, we consider differential and piece-wise linear portfolio allocation frictions, with differential borrowing and lending rates as our most emblematic example. Finally, we present a mutual-fund separation result and illustrate our results with several numerical examples when the adverse jump risk has Beta distribution.

q-fin.MF↗

arXiv2022

Existence of optimal controls for stochastic Volterra equations

We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of stochastic control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes that arise when the kernel appearing in the controlled SVE is singular at zero. The existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel and growth conditions on the running cost functional and the coefficients of the controlled SVEs. Under classical convexity assumptions, we can also deduce the existence of optimal strict controls.

math.OC↗

arXiv2021

ALM for insurers with multiple underwriting lines and portfolio constraints: a Lagrangian duality approach

We study a continuous-time asset-allocation problem for an insurance firm that backs up liabilities from multiple non-life business lines with underwriting profits and investment income. The insurance risks are captured via a multidimensional jump-diffusion process with a multivariate compound Poisson process with dependent components, which allows to model claims that occur in different lines simultaneously. Using Lagrangian convex duality techniques, we provide a general verification-type result for investment-underwriting strategies that maximize expected utility from the dividend payout rate and final wealth over a finite-time horizon. We also study the precautionary effect on earnings retention of risk aversion, prudence, portfolio constraints and multivariate insurance risk. We find an explicit characterization of optimal strategies under CRRA preferences. Numerical results for two-dimensional examples with policy limits illustrate the impact of co-integration for ALM with multiple (dependent and independent) sources of insurance risk.

q-fin.PM↗

arXiv2015

Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics

We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take account of relaxed assumptions such as differential borrowing and lending interest rates or short positions with cash collateral and negative rebate rates. We give suffcient conditions for existence of optimal policies for agents with logarithmic and CRRA power utility. We find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain.

q-fin.PM↗

arXiv2015

On the LP formulation in measure spaces of optimal control problems for jump-diffusions

In this short note we formulate a infinite-horizon stochastic optimal control problem for jump-diffusions of Ito-Levy type as a LP problem in a measure space, and prove that the optimal value functions of both problems coincide. The main tools are the dual formulation of the LP primal problem, which is strongly connected to the notion of sub-solution of the partial integro-differential equation of Hamilton-Jacobi-Bellman type associated with the optimal control problem, and the Krylov regularization method for viscosity solutions.

math.PR↗

arXiv2015

Calculo Estocastico, EDEs y EDPs

This manuscript is a self-contained overview of essential results of stochastic calculus and stochastic differential equations, and their connection with final-value problems for second order linear PDEs.

math.PR↗

arXiv2014

Backward Ornstein-Uhlenbeck transition operators and mild solutions of non-autonomous Hamilton-Jacobi equations in Banach spaces

In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients

math.AP↗

arXiv2014

Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models

We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for existence of optimal policies and find closed-form expressions for the optimal value function for agents with logarithmic and fractional power (CRRA) utility in the case of two-state Markov chains. The main tools are convex duality techniques, stochastic calculus for pure-jump processes and explicit formulae for the moments of telegraph processes with Markov-modulated random jumps.

q-fin.PM↗

arXiv2014

A note on space-time Holder regularity of mild solutions to stochastic Cauchy problems in Lp-spaces

This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\mathcal{O}),$ with $p\geq 2$ and $\mathcal{O}\subset\mathbb{R}^d$ a bounded domain. We find conditions on $p, β$ and $γ$ under which the mild solution has almost surely trajectories in $\mathcal{C}^β([0,T];\mathcal{C}^γ(\bar{\mathcal{O}})).$ These conditions do not depend on the Cameron-Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Z. Brzeźniak (Stoch. Stoch. Rep. Vol. 61, Iss. 3-4, 1997).

math.PR↗

arXiv2010

Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces

We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrisable control sets.

math.PR↗