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We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expected utility of dividend payments over an infinite horizon. By applying a perturbation approach, we obtain the optimal strategy and the value function in closed form for log and power utility. We conduct an economic analysis to investigate the impact of various model parameters and risk aversion on the insurers optimal strategy.
We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utility, including many non-standard utilities as examples. A typical application is the composition of an HARA preference and a piecewise linear payoff in hedge fund
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the r
In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at the origin, dividends give rise to time-d
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage
This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz law and investment opportunities are constant. Healthcare slows