Author: Christian Hipp
Publisher:
ISBN: 9780734013897
Category : Equilibrium (Economics)
Languages : en
Pages : 30
Book Description
Hedging in Incomplete Markets and Optimal Control
Author: Christian Hipp
Publisher:
ISBN: 9780734013897
Category : Equilibrium (Economics)
Languages : en
Pages : 30
Book Description
Publisher:
ISBN: 9780734013897
Category : Equilibrium (Economics)
Languages : en
Pages : 30
Book Description
Pricing and Hedging in Incomplete Markets with Model Uncertainty
Author: Anne Balter
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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.
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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.
Optimal Control and Hedging of Operations in the Presence of Financial Markets
Author: Rene Caldentey
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
We consider the problem of dynamically hedging the profits of a corporation when these profits are correlated with returns in the financial markets. In particular, we consider the general problem of simultaneously optimizing over both the operating policy and the hedging strategy of the corporation. We discuss how different informational assumptions give rise to different types of hedging and solution techniques. Finally, we solve some problems commonly encountered in operations management to demonstrate the methodology.
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
We consider the problem of dynamically hedging the profits of a corporation when these profits are correlated with returns in the financial markets. In particular, we consider the general problem of simultaneously optimizing over both the operating policy and the hedging strategy of the corporation. We discuss how different informational assumptions give rise to different types of hedging and solution techniques. Finally, we solve some problems commonly encountered in operations management to demonstrate the methodology.
Dynamic Hedging in Incomplete Markets
Author: Suleyman Basak
Publisher:
ISBN:
Category : Financial futures
Languages : en
Pages : 0
Book Description
Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete-market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking.
Publisher:
ISBN:
Category : Financial futures
Languages : en
Pages : 0
Book Description
Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete-market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking.
Controlled Markov Processes and Viscosity Solutions
Author: Wendell H. Fleming
Publisher: Springer Science & Business Media
ISBN: 0387310711
Category : Mathematics
Languages : en
Pages : 436
Book Description
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Publisher: Springer Science & Business Media
ISBN: 0387310711
Category : Mathematics
Languages : en
Pages : 436
Book Description
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Robust Hedging in Incomplete Markets
Author: Sally Shen
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
Book Description
We develop a robust optimal dynamic hedging strategy that takes both downside risks and market incompleteness into account for an agent who fears model misspecification. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst case scenario by means of solving a min-max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy.
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
Book Description
We develop a robust optimal dynamic hedging strategy that takes both downside risks and market incompleteness into account for an agent who fears model misspecification. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst case scenario by means of solving a min-max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy.
Optimal Control and Partial Differential Equations
Author: José Luis Menaldi
Publisher: IOS Press
ISBN: 9781586030964
Category : Mathematics
Languages : en
Pages : 632
Book Description
This volume contains more than sixty invited papers of international wellknown scientists in the fields where Alain Bensoussan's contributions have been particularly important: filtering and control of stochastic systems, variationnal problems, applications to economy and finance, numerical analysis... In particular, the extended texts of the lectures of Professors Jens Frehse, Hitashi Ishii, Jacques-Louis Lions, Sanjoy Mitter, Umberto Mosco, Bernt Oksendal, George Papanicolaou, A. Shiryaev, given in the Conference held in Paris on December 4th, 2000 in honor of Professor Alain Bensoussan are included.
Publisher: IOS Press
ISBN: 9781586030964
Category : Mathematics
Languages : en
Pages : 632
Book Description
This volume contains more than sixty invited papers of international wellknown scientists in the fields where Alain Bensoussan's contributions have been particularly important: filtering and control of stochastic systems, variationnal problems, applications to economy and finance, numerical analysis... In particular, the extended texts of the lectures of Professors Jens Frehse, Hitashi Ishii, Jacques-Louis Lions, Sanjoy Mitter, Umberto Mosco, Bernt Oksendal, George Papanicolaou, A. Shiryaev, given in the Conference held in Paris on December 4th, 2000 in honor of Professor Alain Bensoussan are included.
Optimal Dynamic Hedging in Incomplete Futures Markets
Author: Abraham Lioui
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This paper derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case, but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those which obtain under complete markets, incompleteness leads in fact to second best optima.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This paper derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case, but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those which obtain under complete markets, incompleteness leads in fact to second best optima.
Comparison of Some Key Approaches to Hedging in Incomplete Markets
Author: David Heath
Publisher:
ISBN:
Category : Capital market
Languages : en
Pages : 21
Book Description
Publisher:
ISBN:
Category : Capital market
Languages : en
Pages : 21
Book Description
Arbitrage Theory in Continuous Time
Author: Tomas Björk
Publisher: OUP Oxford
ISBN: 0191610291
Category : Business & Economics
Languages : en
Pages : 600
Book Description
The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Publisher: OUP Oxford
ISBN: 0191610291
Category : Business & Economics
Languages : en
Pages : 600
Book Description
The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.