Optimal Investment-Reinsurance Strategies for Insurers with Mean-Reversion and Mispricing under Variance Premium Principle

Abstract

This paper considers a robust optimal reinsurance-investment problem for an insurer with mispricing and model ambiguity. The surplus process is described by a classical Cramér-Lunderg model and the financial market contains a market index, a risk-free asset and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting processes which take into account liquidity constraints. In particular, both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle. By employing the dynamic programming approach, we derive the explicit optimal robust reinsurance-investment strategy and the optimal value function.Open Access , , ,0 ,be a probability space, in which Ω is the state space and  is a σ-algebra on Ω . 0 T > is a fixed constant, representing the time horizon, { } 0 t t≥  is a filtration, which describes the flow Y. Z. Wen DOI: 10.4236/am.2018.97056 808 Applied Mathematics of information over time, the σ-algebra { } t  describes the information available up to time t, and { } 0 t t ≥  satisfies the usual condition (it contains all P-nullsets and is right continuous). We denote P as a reference measure and suppose that all stochastic processes given in the following are assumed to be adapted on this space. aa J represent the value function's partial derivative t t J J wb t J bJ J J

Optimal Reinsurance Strategy for an Insurer and a Reinsurer with Generalized Variance Premium Principle

“…From equation (33), we find that the optimal reinsurance strategy is similar to those in Liang and Yuen [26], Lin and Yang [30], and Wen [31], which considered the optimal reinsurance strategies under variance premium principle only for an insurer.…”