119 research outputs found
Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning
We seek to provide practicable approximations of the two-stage robust
stochastic optimization (RSO) model when its ambiguity set is constructed with
an f-divergence radius. These models are known to be numerically challenging to
various degrees, depending on the choice of the f-divergence function. The
numerical challenges are even more pronounced under mixed-integer first-stage
decisions. In this paper, we propose novel divergence functions that produce
practicable robust counterparts, while maintaining versatility in modeling
diverse ambiguity aversions. Our functions yield robust counterparts that have
comparable numerical difficulties to their nominal problems. We also propose
ways to use our divergences to mimic existing f-divergences without affecting
the practicability. We implement our models in a realistic location-allocation
model for humanitarian operations in Brazil. Our humanitarian model optimizes
an effectiveness-equity trade-off, defined with a new utility function and a
Gini mean difference coefficient. With the case study, we showcase 1) the
significant improvement in practicability of the RSO counterparts with our
proposed divergence functions compared to existing f-divergences, 2) the
greater equity of humanitarian response that our new objective function
enforces and 3) the greater robustness to variations in probability estimations
of the resulting plans when ambiguity is considered
Recommended from our members
To split or not to split: Capital allocation with convex risk measures
Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed
Optimal Real-Time Bidding Strategies
The ad-trading desks of media-buying agencies are increasingly relying on
complex algorithms for purchasing advertising inventory. In particular,
Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey
auctions -- throughout the day for buying ad-inventory with the aim of
maximizing one or several key performance indicators (KPI). The optimization
problems faced by companies building bidding strategies are new and interesting
for the community of applied mathematicians. In this article, we introduce a
stochastic optimal control model that addresses the question of the optimal
bidding strategy in various realistic contexts: the maximization of the
inventory bought with a given amount of cash in the framework of audience
strategies, the maximization of the number of conversions/acquisitions with a
given amount of cash, etc. In our model, the sequence of auctions is modeled by
a Poisson process and the \textit{price to beat} for each auction is modeled by
a random variable following almost any probability distribution. We show that
the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and
that almost-closed form solutions can be found by using a fluid limit.
Numerical examples are also carried out
- …