Related papers: Optimal dividend payments for a two-dimensional in…
We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the…
We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a…
In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
We consider the bail-out optimal dividend problem under fixed transaction costs for a L\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to…
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…
We consider the problem of minimizing the probability of ruin by purchasing reinsurance whose premium is computed according to the mean-variance premium principle, a combination of the expected-value and variance premium principles. We…
We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch…
We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive L\'{e}vy processes, we give a short exposition in which we show the optimality of barrier…
In this paper, a robust optimal reinsurance-investment problem with delay is studied under the $\alpha$-maxmin mean-variance criterion. The surplus process of an insurance company approximates Brownian motion with drift. The financial…
We study an optimal claim reporting problem in a bonus-malus setting. We assume, that the insurance contract consists of two regimes, where reporting a claim leads to a transition to a higher-premium regime, whereas remaining claim-free for…
Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a…
We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover,…
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
Dual risk models are popular for modeling a venture capital or high tech company, for which the running cost is deterministic and the profits arrive stochastically over time. Most of the existing literature on dual risk models concentrated…
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi-Bellman equation and the dynamic programming method. We…
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
In this paper, we study an insurer's reinsurance-investment problem under a mean-variance criterion. We show that excess-loss is the unique equilibrium reinsurance strategy under a spectrally negative L\'{e}vy insurance model when the…
This paper investigates the dynamic reinsurance design problem under the mean-variance criterion, incorporating heterogeneous beliefs between the insurer and the reinsurer, and introducing an incentive compatibility constraint to address…
In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion. Owners can take cash out of the surplus in the form of "dividends", subject to transaction costs. However, if the surplus hits 0 then ruin…