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In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…
Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional…
The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO),…
We study nonsmooth difference-of-convex programs whose subtracted convex term is a finite maximum of smooth convex functions. In this setting, standard DCA iterations may converge to critical points that are not directionally stationary,…
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…
We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds…
One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial…
This study first reviews fuzzy random Portfolio selection theory and describes the concept of portfolio optimization model as a useful instrument for helping finance practitioners and researchers. Second, this paper specifically aims at…
In this paper, we present two variants of DCA (Different of Convex functions Algorithm) to solve the constrained sum of differentiable function and composite functions minimization problem, with the aim of increasing the convergence speed…
In this study, we address the challenge of portfolio optimization, a critical aspect of managing investment risks and maximizing returns. The mean-CVaR portfolio is considered a promising method due to today's unstable financial market…
This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models…
In a series of recent papers, Damiano Brigo, Andrea Pallavicini, and co-authors have shown that the value of a contract in a Credit Valuation Adjustment (CVA) setting, being the sum of the cash flows, can be represented as a solution of a…
Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges,…
This paper concerns a class of constrained difference-of-convex (DC) optimization problems in which, the constraint functions are continuously differentiable and their gradients are strictly continuous. For such nonconvex and nonsmooth…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
This paper studies the optimization of Markov decision processes (MDPs) from a risk-seeking perspective, where the risk is measured by conditional value-at-risk (CVaR). The objective is to find a policy that maximizes the long-run CVaR of…
While researchers in the asset management industry have mostly focused on techniques based on financial and risk planning techniques like Markowitz efficient frontier, minimum variance, maximum diversification or equal risk parity, in…
We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated…