Browsing by Subject "Incomplete Markets"
Now showing 1 - 4 of 4
- Results Per Page
- Sort Options
Item Open Access The Best Gain-Loss Ratio is a Poor Performance Measure(Society for Industrial and Applied Mathematics, 2013-03-06) Biagini, S.; Pinar, M. Ç.The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index, and we provide its dual representation for general probability spaces. However, the gain-loss ratio was designed for finite Ω and works best in that case. For general Ω and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behavior due to the scale invariance property, which does not seem desirable in this context. Such weaknesses definitely prove that the (best) gain-loss is a poor performance measure.Item Open Access Gain-loss based convex risk limits in discrete-time trading(Springer -Verlag, 2011-08) Pinar, M. C.We present an approach for pricing and hedging in incomplete markets, which encompasses other recently introduced approaches for the same purpose. In a discrete time, finite space probability framework conducive to numerical computation we introduce a gain–loss ratio based restriction controlled by a loss aversion parameter, and characterize portfolio values which can be traded in discrete time to acceptability. The new risk measure specializes to a well-known risk measure (the Carr–Geman– Madan risk measure) for a specific choice of the risk aversion parameter, and to a robust version of the gain–loss measure (the Bernardo–Ledoit proposal) for a specific choice of thresholds. The result implies potentially tighter price bounds for contingent claims than the no-arbitrage price bounds. We illustrate the price bounds through numerical examples from option pricing.Item Open Access An integer programming model for pricing American contingent claims under transaction costs(2012) Pınar, M. Ç.; Camcı, A.We study the problem of computing the lower hedging price of an American contingent claim in a finite-state discrete-time market setting under proportional transaction costs. We derive a new mixed-integer linear programming formulation for calculating the lower hedging price. The linear programming relaxation of the formulation is exact in frictionless markets. Our results imply that it might be optimal for the holder of several identical American claims to exercise portions of the portfolio at different time points in the presence of proportional transaction costs while this incentive disappears in their absence.Item Open Access Integration of shipment scheduling decisions for forward and reverse channels in a recoverable item system(Elsevier, 2012-11) Toptal, A.In this paper, we consider the problem of finding the economic shipment quantities of failed and recovered items between a central depot and a collection center to coordinate the flow in both ways. Our model takes an explicit account for the transportation costs and capacities under the assumption of deterministic failure rate of items. The proposed solution provides the optimum shipment quantities, and the level of spare items to be held at the collection center with the objective of minimizing the long-run average total costs subject to a service level.