Optimal investment and reinsurance under exponential forward preferences

TL;DR

This paper develops a model for optimal investment and reinsurance strategies for an insurance company using forward exponential utility in a stochastic environment with market dependence, providing new insights into dynamic risk preferences.

Contribution

It introduces a forward dynamic exponential utility framework for investment and reinsurance, accounting for market dependence and environmental contagion, with detailed characterization and numerical analysis.

Findings

Optimal strategies depend on stochastic factors and market correlation.

Comparison with classical backward utility results highlights differences.

Numerical simulations illustrate strategy features under various scenarios.

Abstract

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.