We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under ...

We consider the problem of hedging the loss of a given portfolio of derivatives using a set of more liquid derivative instruments. We illustrate why the typical mathematical formulation for this hedging problem is ill-posed. We propose to determine a hedging portfolio by minimizing a proportional cost subject to an upper bound on the hedge risk; this bound is typically slightly larger than the ...

This paper introduces a financial hedging model for global environment risks. Our approach is based on portfolio insurance under hedging constraints. Investors are assumed to maximize their expected utilities defined on financial and environmental asset values. The optimal investment is determined for quite general utility functions and hedging constraints. In particular, our results suggest ho...

Drought is an inevitable part of the world’s climate. It occurs in wet as well as in dry regions. Therefore, planning for drought and mitigating its impacts is essential. In this study, a hedging rule is developed using the zero/one mixed integer-programming approach. Furthermore, some procedures are introduced to ease the computational burden inherent in integer programming. Hedging rules are ...

For index-based hedging design, the scatter plot of the hedging contract losses versus the losses to be hedged is generally used to visualize and quantify basis risk. While studying this scatter plot, which does not cluster along the diagonal as desired, a “bundled loss” phenomenon is found. In a setting where both the hedging and the hedged contracts have 100,000 years of simulated losses, thi...

Most authors who studied the problem of option hedging in incomplete markets, and, in particular, in models with jumps, focused on finding the strategies that minimize the residual hedging error. However, the resulting strategies are usually unrealistic because they require a continuously rebalanced portfolio, which is impossible to achieve in practice due to transaction costs. In reality, the ...

In planning and scheduling of production systems manufacturers have two main strategies for responding to uncertainty: they build inventory to hedge against periods in which the production capacity is not suucient to satisfy demand, or they temporarily increase the production capacity. We consider the problem of minimizing the long-run average cost of holding inventory and/or purchasing extra c...

Hedging is widely used to mitigate severe water shortages in the operation of reservoirs during droughts. Rationing is usually instituted with one hedging policy, which is based only on one trigger, i.e., initial storage level or current water availability. It may perform poorly in balancing the benefits of a release during the current period versus those of carryover storage during future drou...

Abstract We analyze the errors arising from discrete rebalancing of the hedging portfolio in exponential Lévy models, and establish the rates at which the expected squared discretization error goes to zero when the length of the rebalancing step decreases. Different hedging strategies and option pay-offs are considered. The case of digital options is studied in detail, and it turns out that in ...

A super-replication problem with a gamma constraint, introduced in [12], is studied in the context of the one-dimensional Black and Scholes model. Several representations of the minimal super-hedging cost are obtained using the characterization derived in [3]. It is shown that the upper bound constraint on the gamma implies that the optimal strategy consists in hedging a conveniently face-lifte...