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This thesis presents the Conditional Value-at-Risk concept and combines an analysis that covers its application as a risk measure and as a vector norm. For both areas of application the theory is revised in detail and examples are given to…
This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be…
This article examines arbitrage investment in a mispriced asset when the mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained investor maximizes a generalization of the Kelly criterion. The optimal differentiable and…
Dynamic real-time optimization (DRTO) is a challenging task due to the fact that optimal operating conditions must be computed in real time. The main bottleneck in the industrial application of DRTO is the presence of uncertainty. Many…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…
This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…
We study distributionally robust Expected Shortfall when the distribution of the underlying is perturbed by a size quantified with optimal transport distance based on the quadratic cost function. In the dual version of the robust…
In binary classification applications, conservative decision-making that allows for abstention can be advantageous. To this end, we introduce a novel approach that determines the optimal cutoff interval for risk scores, which can be…
Online portfolio selection research has so far focused mainly on minimizing regret defined in terms of wealth growth. Practical financial decision making, however, is deeply concerned with both wealth and risk. We consider online learning…
Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…
We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
In this paper, we investigate the optimal management of defined contribution (abbr. DC) pension plan under relative performance ratio and Value-at-Risk (abbr. VaR) constraint. Inflation risk is introduced in this paper and the financial…
We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that…
Based on a point of view that solvency and security are first, this paper considers regular-singular stochastic optimal control problem of a large insurance company facing positive transaction cost asked by reinsurer under solvency…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. The trader encounters a trade-off between the transaction costs…
Varying-coefficient functional linear models consider the relationship between a response and a predictor, where the response depends not only the predictor but also an exogenous variable. It then accounts for the relation of the predictors…