The paper is concerned with stochastic control problems of finite time horizon whose running cost function is of superlinear growth with respect to the control variable. We prove that, as the time horizon tends to infinity, the value function converges to a function of variable separation type...

We consider an optimal investment and consumption problem for a Black–Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamic programming approach leads...

We consider in this paper that the reserve of an insurance company follows the classical model, in which the aggregate claim amount follows a compound Poisson process. Our goal is to minimize the ruin probability of the company assuming that the management can invest dynamically part of the...

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse...

We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax–Oleĭnik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a...

We consider an investor who wants to select his optimal consumption, investment and insurance policies. Motivated by new insurance products, we allow not only the financial market but also the insurable loss to depend on the regime of the economy. The objective of the investor is to maximize his...

Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems...

We consider in this paper that the reserve of an insurance company follows the classical model, in which the aggregate claim amount follows a compound Poisson process. Our goal is to minimize the ruin probability of the company assuming that the management can invest dynamically part of the...

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant...

We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg model with arbitrary claim-size distribution. Our objective is to find the dividend payment policy which maximizes the cumulative expected...