Option Pricing by Mathematical Programming

Financial options typically incorporate times of exercise. Alternatively, they embody setup costs or indivisibilities. Such features lead to planning problems with integer decision variables. Provided the sample space be finite, it is shown here that integrality constraints can often be relaxed. In fact, simple mathematical programming, aimed at arbitrage or replication, may find optimal exercise, and bound or identify option prices. When the asset market is incomplete, the bounds system from nonlinear pricing functionals

Equilibrium Programming Using Proximal-Like Algorithms

We consider problems where solutions -- called equilibria -- emerge as fixed points of an extremal mapping. Examples include convex programming, convex -- concave saddle problems, many noncooperative games, and quasi -- monotone variational inequalities. Using Bregman functions we develop proximal -- like algorithms for finding equilibria. At each iteration we allow numerical errors or approximate solutions

Greenhouse Gases, Cooperation, and Exchange

Emission of uniformly dispersed greenhouse gases is construed here as a cooperative production game, featuring side-payments, quota exchange, uncertainty, and multi-period planning. Stochastic programming offers good instruments to analyze such games. "Absent" efficient markets for emissions, such programming may help to imitate market-like, price-based transfers among concerned parties. "Present" appropriate markets, it may predict equilibrium outcomes. In both cases, shadow values of aggregate emissions define side-payments or prices that yield core solutions

Noncooperative Convex Games: Computing Equilibrium By Partial Regularization

A class of non-cooperative constrained games is analyzed for which the Ky Fan function is convex-concave. Nash equilibria of such games correspond to diagonal saddle points of the said function. This feature is exploited in designing computational algorithms for finding such equilibria

On Mutual Insurance

Owners of stochastic assets can pool their endowments to smoothen and insure individual payoffs across outcomes and time. We explore, in such a setting, how contingent shadow prices on aggregate resources can be used for three purposes: First, to design mutual contracts for risk averse agents; second, to quantify the malfunctioning of such contracts when there are risk lovers (or scale economies); and third, to estimate reasonable premiums for insurance offered by outside agents

Learning in Potential Games

We consider repeated play of so-called potential games. Numerous modes of play are shown to yield Nash equilibrium in the long run. We point to procedures that can account for society-wide constraints concerning efficiency

Price Expectations, Cobwebs and Stability

There is given a market for several perishable goods, supplied under technological randomness and price uncertainty. We study whether and how producers eventually may learn rational price expectations. The model is of cobweb type. Its dynamics fit standard forms of stochastic approximation. Relying upon quite weak and natural assumptions we prove new convergence results

Investment, Uncertainty, and Cooperation

This paper explores some cooperative aspects of investments in uncertain, real options. Key production factors are assumed transferable. They may reflect property or user rights. Emission of pollutants and harvest of renewable resources are cases in point. Of particular interest are alternative projects or technologies that provide inferior but anti-correlated returns. Any such project stabilizes the aggregate proceeds. Therefore, given widespread risk exposure and aversion, that project's worth may embody an extra bonus. The setting is formalized as a stochastic production game. Granted no economies of scale of such games are quite tractable in analysis, computation, and realization. A core imputation comes in terms of contingent shadow prices that equilibrate competitive, endogenous markets. The said prices emerge as optimal dual solutions to coordinated production programs, featuring pooled resources - and also via adaptive procedures. Extra value - or an insurance premium - adds to any project whose yield is negatively associated with the aggregate

Existence Results and Finite Horizon Approximates for Infinite Horizon Optimization Problems

The paper deals with infinite horizon optimization problems. The existence of optimal solutions is obtained as a consequence of an asymptotic growth condition. We also exhibit finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long-term optimal trajectories