We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below target growth rate. From mathematical viewpoint, this is large deviation control problem. This will be shown relate risk-sensitive stochastic for sufficiently time horizon. Indeed, in our theorem we state duality relation between above two problems. Furthermore, under multidimensional linear Gaussian model obtain explicit solutions primal

We consider a consumption problem with an infinite time horizon to optimize the discounted expected power utility. The returns and volatilities of assets are random affected by some economic factors, modeled as diffusion process. becomes standard control problem. derive Hamilton--Jacobi--Bellman (HJB) equation study its solutions. In Part I, under weak conditions we prove existence solution for this HJB when assume ordered pair sub/supersolution. To construct sub/supersolution, also...

Abstract We consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of and terminal wealth. treat stochastic factor model in which mean returns risky assets depend linearly on underlying economic factors formulated as solutions linear differential equations. discuss partial information case cannot observe process uses only past assets. Then our is control with information. derive Hamilton–Jacobi–Bellman...

We consider the Merton consumption problem on a finite time horizon to optimize discounted expected power utility of and terminal wealth in risk-averse cases. The returns volatilities assets are random affected by some economic factors, modeled as diffusion process. becomes standard stochastic control problem. derive Hamilton--Jacobi--Bellman (HJB) equation study its solutions. Under general conditions we construct suitable subsolution--supersolution pair. prove existence uniqueness solution...

We consider an optimal consumption problem where investor tries to maximize the infinite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. treat a stochastic factor model such that mean returns risky assets depend on underlying economic factors formulated as solution differential equation. Using dynamic programming principle, we derive Hamilton--Jacobi--Bellman (HJB) equation and study its solutions. In part I, prove existence classical for HJB under...

The risk-sensitive asset management problem with a finite horizon is studied under financial market model having Wishart autoregressive stochastic factor, which positive-definite symmetric matrix-valued. This has the following interesting features: 1) it describes stochasticity of covariance structure, interest rates, and risk premium risky assets; 2) admits explicit representations solution to problem.

In this paper, we consider the problem of optimal investment by an insurer. The wealth insurer is described a Cramér–Lundberg process. invests in market consisting bank account and m risky assets. mean returns volatilities assets depend linearly on economic factors that are formulated as solutions linear stochastic differential equations. Moreover, preferences exponential. With setting, Hamilton–Jacobi–Bellman equation derived via dynamic programming approach has explicit solution found...

In this article, we consider a modification of the Karatzas–Pikovsky model insider trading. Specifically, suppose that agent influences long/medium-term evolution Black–Scholes type through drift stochastic differential equation. We say is using portfolio leading to partial equilibrium if following three properties are satisfied: (a) used by leads stock price which semimartingale under his/her own filtration and enlarged with final price; (b) optimal in sense it maximises logarithmic utility...

<p style='text-indent:20px;'>We propose the stochastic factor model of optimal investment and reinsurance insurers where wealth processes are described by a bank account risk asset for Cramér-Lundberg process reinsurance. The optimization is obtained through maximizing exponential utility. Owing to claims driven Poisson process, proposed problem naturally treated as jump-diffusion control problem. Applying dynamic programming, we have Hamilton-Jacobi-Bellman (HJB) equations...

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer with delay under $ 4/2 stochastic volatility model. Indeed, objective is to maximize expected power utility terminal wealth average on finite time horizon. The other growth rate per unit infinite described by approximation classical Cramér–Lundberg process. Then, these problems can be formulated as control delay. A pair forward-backward differential equations that derived via maximum principle...

In this paper, we give some numerical results related to Hata and Yasuda [1] that constructed an optimal investment reinsurance strategies of maximizing the expected power utility maximization problem for insurer. our experiments, use pathwise analysis Monte-Carlo simulation, compare four cases which have or do not reinsurance. And as performance criteria, adopt return, risk, Sharp ratio, terminal wealth, values their ranking.