Geometric Brownian motion

Financial economics

Physics

Accounting

Economy

Econometrics

Actuarial science

Economics

Reinsurance

Variance (accounting)

Pure mathematics

Jump process

Jump diffusion

Service (business)

Jump

Portfolio

Applied mathematics

Mathematics

Efficient frontier

Stochastic differential equation

Quantum mechanics

Diffusion process

Stochastic volatility

Volatility (finance)

Affine transformation

Scandinavian Actuarial Journal

This paper considers an optimal asset-liability management (ALM) problem for an insurer under the mean-variance criterion. It is assumed that the value of liabilities is described by a geometric Brownian motion (GBM). The insurer's surplus process is modeled by a general jump process generated by a marked point process. The financial market consists of one risk-free asset and n risky assets with the risk premium relying on an affine diffusion factor process. By transferring a proportion of insurance risk to a reinsurer and investing the surplus into the financial market, the insurer aims to maximize the expected terminal net wealth and, at the same time, minimize the corresponding variance of the terminal net wealth. By using a backward stochastic differential equation (BSDE) approach, closed-form expressions for both the efficient strategy and efficient frontier are derived. To illustrate the main results, we study an example with the Heston stochastic volatility (SV) model and numerically analyze the economic behavior of the efficient frontier. Finally, a generalization of the Mutual Fund Theorem is obtained.

Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option