Risk-based optimal portfolio of an insurer with regime switching and noisy memory

TL;DR

This paper develops a risk-based optimal investment model for an insurer considering regime switching, jump diffusion, and noisy memory, solved via backward stochastic differential equations with analytical solutions for specific cases.

Contribution

It introduces a novel regime-switching jump diffusion model with noisy memory for insurer investment, solved through a BSDE approach, providing analytical solutions for particular penalty functions.

Findings

Analytical solutions derived for the game problem.

Numerical example illustrating the model's application.

Model captures complex market dynamics with regime switching and memory effects.

Abstract

In this paper, we consider a risk-based optimal investment problem of an insurer in a regime-switching jump diffusion model with noisy memory. Using the model uncertainty modeling, we formulate the investment problem as a zero-sum, stochastic differential delay game between the insurer and the market, with a convex risk measure of the terminal surplus and the Brownian delay surplus over a period $[T-\varrho,T]$. Then, by the BSDE approach, the game problem is solved. Finally, we derive analytical solutions of the game problem, for a particular case of a quadratic penalty function and a numerical example is considered.