Related papers: Singular Control in a Cash Management Model with A…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a…
A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to…
Dybvig (1988a,b) solves in a complete market setting the problem of finding a payoff that is cheapest possible in reaching a given target distribution ("cost-efficient payoff"). In the presence of ambiguity, the distribution of a payoff is,…
We study a dynamic asset pricing problem in which a representative agent is ambiguous about the aggregate endowment growth rate and trades a risky stock, human capital, and a risk-free asset to maximize her preference value of consumption…
Congestion game is a widely used model for modern networked applications. A central issue in such applications is that the selfish behavior of the participants may result in resource overloading and negative externalities for the system…
The traditional difficulty about stochastic singular control is to characterize the regularities of the value function and the optimal control policy. In this paper, a multi-dimensional singular control problem is considered. We found the…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
We investigate the well-posedness of a general class of singular stochastic control problems in which controls are processes of finite variation. We develop an abstract framework, which we then apply to storage management and portfolio…
We introduce a setup of model uncertainty in discrete time. In this setup we derive dual expressions for the super--replication prices of game options with upper semicontinuous payoffs. We show that the super--replication price is equal to…
Cash management is concerned with optimizing the short-term funding requirements of a company. To this end, different optimization strategies have been proposed to minimize costs using daily cash flow forecasts as the main input to the…
We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish…
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
Stablecoins promise par convertibility, yet issuers must balance immediate liquidity against yield on reserves to keep the peg credible. We study this treasury problem as a continuous-time control task with two instruments: reallocating…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…