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In this paper, the problem of load uncertainty in compliance problems is addressed where the uncertainty is described in the form of a set of finitely many loading scenarios. Computationally more efficient methods are proposed to exactly…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control…
In this paper, we formulate cyber risk management and mitigation as a stochastic optimal control problem under a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model. To capture the dynamics and interplay of management and…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
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,…
Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is…
This paper studies flexible multi-facility capacity expansion with risk aversion. In this setting, the decision maker can periodically expand the capacity of facilities given observations of uncertain demand. We model this situation as a…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal…
The nuclear fuel loading pattern optimization problem belongs to the class of large-scale combinatorial optimization. It is also characterized by multiple objectives and constraints, which makes it impossible to solve explicitly. Stochastic…
We present an optimization-based approach to stochastic control problems with nonclassical information structures. We cast these problems equivalently as optimization prob- lems on joint distributions. The resulting problems are necessarily…
The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise…
In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…
The rapid expansion of wind and solar energy leads to an increasing volatility in the electricity generation. Previous studies have shown that storage devices provide an opportunity to balance fluctuations in the power grid. An economical…