Rudabeh Meskarian

Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization

Inspired by the successful applications of the stochastic optimization with second order stochastic dominance (SSD) model in portfolio optimization, we study new numerical methods for a general SSD model where the underlying functions are not necessarily linear. Specifically, we penalize the SSD constraints to the objective under Slater’s constraint qualification and then apply the well known stochastic approximation (SA) method and the level function method to solve the penalized problem. Both methods are iterative: the former requires to calculate an approximate subgradient of the objective function of the penalized problem at each iterate while the latter requires to calculate a subgradient. Under some moderate conditions, we show that w.p.1 the sequence of approximated solutions generated by the SA method converges to an optimal solution of the true problem. As for the level function method, the convergence is deterministic and in some cases we are able to estimate the number of iterations for a given precision. Both methods are applied to portfolio optimization problem where the return functions are not necessarily linear and some numerical test results are reported.

Exact Penalization, Level Function Method, and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance Constraints

Level function methods and cutting-plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance (SSD) constraints. A level function method requires an exact penalization setup because it can only be applied to the objective function, not the constraints. Slater constraint qualification (SCQ) is often needed for deriving exact penalization. It is well known that SSD usually does not satisfy SCQ and various relaxation schemes have been proposed so that the relaxed problem satisfies the SCQ. In this paper, we show that under some moderate conditions the desired constraint qualification can be guaranteed through some appropriate reformulation of the constraints rather than relaxation. Exact penalization schemes based on

Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints

L_1

A facility location model for analysis of current and future demand for sexual health services

-norm and

REGIONAL CAPACITY PLANNING FOR DEMENTIA CLINIC DIAGNOSIS

L_\infty

Beyond normality: A cross moment-stochastic user equilibrium model

-norm are subsequently derived through Robinsons error bound on convex systems and Clarkes exact penalty function theorem. Moreover, we propose a modified cutting-plane method which constructs a cutting-plane through t...

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

Reward-risk ratio optimization is an important mathematical approach in finance. We revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken to mitigate the risk arising from ambiguity of the true distribution. We consider a distributionally robust reward-risk ratio optimization model varied from the ex ante Sharpe ratio where the ambiguity set is constructed through prior moment information and the return function is not necessarily linear. We transform the robust optimization problem into a nonlinear semi-infinite programming problem through standard Lagrange dualization and then use the well-known entropic risk measure to construct an approximation of the semi-infinite constraints. We solve the latter by an implicit Dinkelbach method. Finally, we apply the proposed robust model and numerical scheme to a portfolio optimization problem and report some preliminary numerical ...

Using simulation to help hospitals reduce emergency department waiting times: examples and impact

In this paper we address the clinic location selection problem for a fully integrated Sexual Health Service across Hampshire. The service provides outpatient services for Genito-Urinary Medicine, contraceptive and reproductive health, sexual health promotion and a sexual assault referral centre. We aim to assist the planning of sexual health service provision in Hampshire by conducting a location analysis using both current and predicted patient need. We identify the number of clinic locations required and their optimal geographic location that minimise patient travel time. To maximise the chances of uptake of results we validate the developed simple algorithm with an exact method as well as three well-known, but complex meta-heuristics. The analysis was conducted using car travel and public transport times. Two scenarios were considered: current clinic locations only; and anywhere within Hampshire. The results show that the clinic locations could be reduced from 28 to 20 and still keep 90% of all patient journeys by public transport (e.g. by bus or train) to a clinic within 30 minutes. The number of clinics could be further reduced to 8 if the travel time is based on car travel times within 15 minutes. Results from our simple solution method compared favourably to the exact solution as well as the complex meta-heuristics.

Using Health Systems Analytics to Help the NHS

Pre-index assessment period ACB score, mean 6 SD 0.89 6 1.39 1.02 6 1.52 <0.0001 ACB score distribution, n (%) ACB score 1⁄4 0 37,151 (56.0%) 34,378 (51.8%) ACB score 1⁄4 1 15,562 (23.4%) 16,353 (24.6%) ACB score 1⁄4 2 5,374 (8.1%) 6,105 (9.2%) ACB score 1⁄4 3 4,296 (6.5%) 4,636 (7.0%) ACB score 4 4,016 (6.0%) 4,927 (7.4%) Post-index assessment period ACB score, mean 6 SD 0.94 6 1.43 1.05 6 1.53 <0.0001 ACB score distribution, n (%) ACB score 1⁄4 0 35,711 (53.8%) 33,397 (50.3%) ACB score 1⁄4 1 16,079 (24.2%) 16,665 (25.1%) ACB score 1⁄4 2 5,719 (8.6%) 6,406 (9.6%) ACB score 1⁄4 3 4,545 (6.8%) 4,851 (7.3%) ACB score 4 4,345 (6.5%) 5,080 (7.7%) Change in ACB score, mean 6 SD 0.06 6 1.09 0.03 6 1.17 0.0005