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We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing…
We introduce a dynamic optimization framework to analyze optimal portfolio allocations within an information driven contagious distress model. The investor allocates his wealth across several stocks whose growth rates and distress…
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has…
In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton-Jacobi-Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the…
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…
We are concerned with optimal control strategies subject to uncertain demands. An Ornstein-Uhlenbeck process describes the uncertain demand. The transport within the supply system is modeled by the linear advection equation. We consider…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider…
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of…
We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We solve the stochastic control problem…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between…
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular,…
We consider a semilinear equation linked to the finite horizon consumption - investment problem under the stochastic factor framework and we prove it admits a classical solution and provide all obligatory estimates to successfully apply a…
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…