Efficient Hedging in Incomplete Markets Under Model Uncertainty PDF Download
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Author: Michael Kirch
Publisher:
ISBN:
Category :
Languages : en
Pages : 137
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Author: Michael Kirch
Publisher:
ISBN:
Category :
Languages : en
Pages : 137
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Book Description
Author: Anne Balter
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. Our set-up is that we postulate an agent who wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the agent is concerned about model misspecification. This robust optimal control problem under model uncertainty leads to (i) risk-neutral pricing for the traded risky assets, and (ii) adjusting the drift of the nontraded risk drivers in a conservative direction. The direction depends on the agent's long or short position, and the adjustment that ensures a robust strategy leads to what is known as "actuarial" or "prudential" pricing. Our results extend to a multivariate setting. We prove existence and uniqueness of the robust price in an incomplete market via the link between the semilinear partial differential equation and backward stochastic differential equations.
Author: Wouter J. Den Haan
Publisher:
ISBN:
Category : Stock exchanges
Languages : en
Pages : 57
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Author: Dirk Becherer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We derive robust good-deal hedges and valuations under combined model ambiguity about the drift and volatility of asset prices for incomplete markets. Good-deal valuations are determined such that not just opportunities for arbitrage but also for overly attractive reward-to-risk ratios are excluded, by restricting instantaneous Sharpe ratios for any market extension by derivatives. From a finance point of view, this permits for hedges and valuation bounds than are less extreme (respectively expensive) than those from the more fundamental approach of almost-sure superhedging and its corresponding no-arbitrage bounds. In mathematical terms, it demands however that not just ambiguities about the volatility but also about the drift become relevant. For general measurable contingent claims, possibly path-dependent, the solutions are described by 2nd-order backward stochastic differential equations with non-convex drivers, building on recent research progress on non-linear kernels. Hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures, uniformly over all priors.
Author: Alain Bensoussan
Publisher: Elsevier
ISBN: 0080931006
Category : Mathematics
Languages : en
Pages : 743
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Book Description
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field
Author: Christian Hipp
Publisher:
ISBN: 9780734013897
Category : Equilibrium (Economics)
Languages : en
Pages : 30
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Author: Yuhong Xu
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
In this paper I investigate financial markets with drift and volatility uncertainties. Appropriate definitions of arbitrage for super and sub-hedging strategies are presented such that the super and sub-hedging prices are reasonable. Especially the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty. The Profit&Loss (P&L for short) of super(sub)-hedging is derived to be in fact the penalty term K with finite-variance arising in the super(sub)-hedging strategy. The ask-bid spread is hence an accumulation of the superhedging P&L and the subhedging P&L.Asset allocation under constant absolute risk aversion (CARA) utility is investigated with ambiguous volatility and subjective risk premium. I show that ambiguity aversion of a rational individual decreases her market participation. The aggregate premium is computed explicitly which is decomposed into three parts. Opposite signs between the rates of ambiguity premium and risk premium demonstrate that a decrease in ambiguity premium on volatility gives rise to an increase in risk premium.Kelly criterion for the wealth process to reach a goal is also studied under such ambiguous market. Ambiguity of stock appreciation rate results in investors' withdraw from markets whereas in a single-priced market, investors always trade with the market if no short-sale constraints and no transaction cost.
Author: Chao Qiu
Publisher:
ISBN:
Category :
Languages : en
Pages : 181
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Book Description
This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate options. To better understand the effect of the pricing method, we also compared the results with those generated from two other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method. We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under study, and mean variance hedging. We also develop a more general tool of tail ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where the regime switching process brings uncertainty.
Author: Joachim Rosenthal
Publisher: Springer Science & Business Media
ISBN: 0387216960
Category : Science
Languages : en
Pages : 508
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Book Description
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
Author: Radu Sebastian Tunaru
Publisher: World Scientific
ISBN: 9814663425
Category : Business & Economics
Languages : en
Pages : 382
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Book Description
The financial systems in most developed countries today build up a large amount of model risk on a daily basis. However, this is not particularly visible as the financial risk management agenda is still dominated by the subprime-liquidity crisis, the sovereign crises, and other major political events. Losses caused by model risk are hard to identify and even when they are internally identified, as such, they are most likely to be classified as normal losses due to market evolution.Model Risk in Financial Markets: From Financial Engineering to Risk Management seeks to change the current perspective on model innovation, implementation and validation. This book presents a wide perspective on model risk related to financial markets, running the gamut from financial engineering to risk management, from financial mathematics to financial statistics. It combines theory and practice, both the classical and modern concepts being introduced for financial modelling. Quantitative finance is a relatively new area of research and much has been written on various directions of research and industry applications. In this book the reader gradually learns to develop a critical view on the fundamental theories and new models being proposed.
