Optimized Investment Strategy and Proportional Reinsurance of Insurance Company under Ornstein–Uhlenbeck and Geometric Brownian Motion Models.
Publication Date: 02/11/2024
Author(s): I. M. Mankilik, S. A. Ihedioha.
Volume/Issue: Volume 7 , Issue 4 (2024)
Abstract:
In this work we investigated the optimization of an insurer’s investment strategy and the proportional reinsurance rate of his portfolio under power utility preference in the cases of correlating and non-correlating Brownian motions. The market in which insurer traded two assets; a risky asset which price process was governed by the geometric Brownian motion (GBM) and riskless asset that had its price driven by the Ornstein-Uhlenbeck stochastic model. We derived the required Hamilton-Jacobi-Bellman Equation (HJB) by applying the maximum principle of dynamic programming and the elimination of dependency on variables was used to obtain the analytic solutions of optimizes investment strategy and the proportional reinsurance rate.
Keywords:
Optimized investment strategy, Proportional reinsurance, Insurance company, Ornstein–Uhlenbeck model, Geometric Brownian motion model.
