Invited Session Tue.2.H 3027

Tuesday, 13:15 - 14:45 h, Room: H 3027

Cluster 7: Finance & economics [...]

Financial optimization


Chair: Yuying Li



Tuesday, 13:15 - 13:40 h, Room: H 3027, Talk 1

Yuying Li
A novel method for computing an optimal VaR portfolio

Coauthors: Thomas F. Coleman, Jiong Xi


Computing an optimal portfolio with minimum value-at-risk (VaR) is computationally challenging since there are many local minimizers. We consider a nonlinearly constrained optimization formulation directly based on VaR definition in which VaR is defined by a probabilistic inequality constraint. We compute an optimal portfolio using a sequence of smooth approximations to the nonlinear inequality constraint. The proposed sequence of smooth approximations gradually becomes more nonconvex in an attempt to track the global optimal portfolio. Computationally comparisons will be presented to illustrate the accuracy and efficiency of the proposed method.



Tuesday, 13:45 - 14:10 h, Room: H 3027, Talk 2

Qihang Lin
First-order algorithms for optimal trade execution with dynamic risk measures

Coauthor: Javier Pena


We propose a model for optimal trade execution in an illiquid market that minimizes a coherent dynamic risk of the sequential transaction costs. The prices of the assets are modeled as a discrete random walk perturbed by both temporal and permanent impacts induced by the trading volume. We show that the optimal strategy is time-consistent and deterministic if the dynamic risk measure satisfies a Markov property. We also show that our optimal execution problem can be formulated as a convex program, and propose an accelerated first-order method that computes its optimal solution. The efficiency and scalability of our approaches are illustrated via numerical experiments.



Tuesday, 14:15 - 14:40 h, Room: H 3027, Talk 3

Somayeh Moazeni
Regularized robust optimization for optimal portfolio execution

Coauthors: Thomas F. Coleman, Yuying Li


An uncertainty set is a crucial component in robust optimization. Unfortunately, it is often unclear
how to specify it precisely. Thus it is important to study sensitivity of the robust solution to variations
in the uncertainty set, and to develop a method which improves stability of the robust solution. To address these issues, we focus on uncertainty in the price impact parameters in the optimalportfolio execution problem. We illustrate that a small variation in the uncertainty set may result in a large change in the robust solution. We then propose a regularized robust optimization formulation which yields a solution with a better stability property than the classical robust solution. In this approach, the
uncertainty set is regularized through a regularization constraint. The regularized robust
solution is then more stable with respect to variation in the uncertainty set specification, in addition to
being more robust to estimation errors in the price impact parameters. We show that the regularized robust solution can be computed efficiently using convex optimization. We also study implications of the regularization on the
solution and its corresponding execution cost.


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