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Abstract: In this paper the utility optimization problem for a general insurance modelis studied. The reserve process of the insurance company is described by astochastic differential equation driven by a Brownian motion and a Poissonrandom measure, representing the randomness from the financial market and theinsurance claims, respectively. The random safety loading and stochasticinterest rates are allowed in the model so that the reserve process isnon-Markovian in general. The insurance company can manage the reserves throughboth portfolios of the investment and a reinsurance policy to optimize acertain utility function, defined in a generic way. The main feature of theproblem lies in the intrinsic constraint on the part of reinsurance policy,which is only proportional to the claim-size instead of the current level ofreserve, and hence it is quite different from the optimalinvestment-consumption problem with constraints in finance. Necessary andsufficient conditions for both well posedness and solvability will be given bymodifying the ``duality method- in finance and with the help of thesolvability of a special type of backward stochastic differential equations.

Autor: Yuping Liu, Jin Ma

Fuente: https://arxiv.org/

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