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Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process

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  • Shen, Yang
  • Zou, Bin

Abstract

We consider an optimal investment and risk control problem for an insurer under the mean–variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem related to the original MV problem, and obtain the optimal strategy and the value function to the new problem in closed-form. We compare our formulation and optimal strategy to those under the precommitment and game-theoretic framework. Numerical studies show that, when the financial market is negatively correlated with the risk process, optimal investment may involve short selling the risky asset and, if that happens, a less risk averse insurer short sells more risky asset.

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  • Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    • Handle: RePEc:eee:insuma:v:97:y:2021:i:c:p:68-80
    DOI: 10.1016/j.insmatheco.2021.01.004
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    2. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2022. "Stackelberg differential game for insurance under model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 128-145.

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    More about this item

    Keywords

    Optimal reinsurance; Jump–diffusion; Hamilton–Jacobi–Bellman equation; Time-consistent control; Precommitment;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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