arXiv subjects

Benedetta Salterini

Publications and source records attributed to Benedetta Salterini.

4 recordsLinked to original sources

arXiv2025

Indifference pricing of pure endowments in a regime-switching market model

In this paper, we study the exponential utility indifference pricing of pure endowment policies within a stochastic-factor model for an insurer who also invests in a financial market. Our framework incorporates a hazard rate modeled as an observable diffusion process, while the risky asset price follows a jump-diffusion process driven by a continuous-time finite-state Markov chain, effectively capturing different economic regimes. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we derive optimal investment strategies with and without the insurance derivative and characterize the indifference price as a classical solution to a linear partial differential equation (PDE). Additionally, we provide a probabilistic representation of the indifference price via an extension of the Feynman-Kac formula and show that it satisfies a suitable backward PDE. Finally, some numerical experiments are conducted to perform sensitivity analyses, highlighting the impact of key model parameters.

q-fin.PM↗

arXiv2022

Optimal investment and reinsurance under exponential forward preferences

We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible dependence between the financial and insurance markets. Specifically, we assume that the asset price process dynamics and the claim arrival intensity are both affected by a common stochastic process and we account for a possible environmental contagion effect through the non-zero correlation parameter between the underlying Brownian motions driving the asset price process and the stochastic factor dynamics. By stochastic control techniques, we construct a forward dynamic exponential utility, and we characterize the optimal investment and reinsurance strategy. Moreover, we investigate in detail the zero-volatility case and provide a comparison analysis with classical results in an analogous setting under backward utility preferences. We also discuss an extension of the conditional certainty equivalent. Finally, we perform a numerical analysis to highlight some features of the optimal strategy.

q-fin.MF↗

arXiv2022

Some Optimisation Problems in Insurance with a Terminal Distribution Constraint

In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time $T$ follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases: in discrete and continuous time settings. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. To achieve a certain level of sustainability (i.e. the collected premia should be sufficient to buy reinsurance and to pay the occurring claims) the initial capital is set to be zero. We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level $α$. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.

q-fin.MF↗

arXiv2021

Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences

In this paper we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

q-fin.PM↗