We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time with nondominated priors and finite time horizon in a diffusion model. We assume that the uncertainty set is compact and time dependent on $[0,T]$. We solve the robust optimization problem explicitly both when the investor’s utility is of … Read more
This paper analyzes the interplay of transmission and storage investments in a multistage game that we translate into a bilevel market model. In particular, on the first level we assume that a transmission system operator chooses an optimal line investment and a corresponding optimal network fee. On the second level we model competitive firms that … Read more
This paper analyzes the effects of storage facilities on optimal zonal pricing in competitive electricity markets. In particular, we propose a zonal pricing model that comprises consumers, producers, and storage facilities on a network with constrained transmission capacities. In its two limit cases, our zonal pricing model includes the reference nodal pricing model as well … Read more
This paper addresses the Entropic Value-at-Risk (EVaR), a recently introduced coherent risk measure. It is demonstrated that the norms induced by EVaR induce the same Banach spaces, irrespective of the confidence level. Three spaces, called the primal, dual, and bidual entropic spaces, corresponding with EVaR are fully studied. It is shown that these spaces equipped … Read more
In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the Mangasarian-Fromovitz and the basic constraint qualification, we show that any … Read more
We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more
Dynamic portfolio optimization has a vast literature exploring different simplifications by virtue of computational tractability of the problem. Previous works provide solution methods considering unrealistic assumptions, such as no transactional costs, small number of assets, specific choices of utility functions and oversimplified price dynamics. Other more realistic strategies use heuristic solution approaches to obtain suitable … Read more
We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more
We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more
We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming (SDDP) … Read more