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Lévy Processes in Finance: Theory, Numerics, and Empirical Facts
, 2000
"... Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible distribution can be chosen as the increment distribution over periods of time ∆t. On the other hand, they have ..."
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Cited by 81 (2 self)
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Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible distribution can be chosen as the increment distribution over periods of time ∆t. On the other hand, they have a simple structure in comparison with general semimartingales. Thus stochastic models based on Lévy processes often allow for analytically or numerically tractable formulas. This is a key factor for practical applications. This thesis is divided into two parts. The first, consisting of Chapters 1, 2, and 3, is devoted to the study of stock price models involving exponential Lévy processes. In the second part, we study term structure models driven by Lévy processes. This part is a continuation of the research that started with the author's diploma thesis Raible (1996) and the article Eberlein and Raible (1999). The content of the chapters is as follows. In Chapter 1, we study a general stock price model where the price of a single stock follows an exponential Lévy process. Chapter 2 is devoted to the study of the Lévy measure of infinitely divisible distributions, in particular of generalized hyperbolic distributions. This yields information about what changes in the distribution of a generalized hyperbolic Lévy motion can be achieved by a locally equivalent change of the underlying probability measure. Implications for
On the Range of Options Prices
, 1997
"... this paper we consider the valuation of an option with time to expiration T and payoff function g which is a convex function (as is a European call option), and constant interest rate r, in the case where the underlying model for stock prices (S t ) is a purely discontinuous process (hence typicall ..."
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Cited by 51 (6 self)
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this paper we consider the valuation of an option with time to expiration T and payoff function g which is a convex function (as is a European call option), and constant interest rate r, in the case where the underlying model for stock prices (S t ) is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for "most" such models, the range of the values of the option, using all possible equivalent martingale measures for the valuation, is the interval (e
The VarianceOptimal Martingale Measure for Continuous Processes
 Bernoulli
, 1996
"... Abstract. We prove that for continuous stochastic processes S based on ( � F�P) for which there is an equivalent martingale measure Q 0 with squareintegrable density dQ 0 =dPwe have that the socalled "variance optimal " martingale measure Qopt for which the density dQopt =dPhas minimal ..."
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Cited by 51 (2 self)
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Abstract. We prove that for continuous stochastic processes S based on ( � F�P) for which there is an equivalent martingale measure Q 0 with squareintegrable density dQ 0 =dPwe have that the socalled "variance optimal " martingale measure Qopt for which the density dQopt =dPhas minimal L2 (P)norm is automatically equivalenttoP. The result is then applied to an approximation problem arising in Mathematical Finance. 1.
Valuation and hedging of life insurance liabilities with systematic mortality risk.
 Insurance: Mathematics and Economics,
, 2006
"... Abstract. This paper considers the problem of valuating and hedging life insurance contracts that are subject to systematic mortality risk in the sense that the mortality intensity of all policyholders is affected by some underlying stochastic processes. In particular, this implies that the insura ..."
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Cited by 47 (3 self)
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Abstract. This paper considers the problem of valuating and hedging life insurance contracts that are subject to systematic mortality risk in the sense that the mortality intensity of all policyholders is affected by some underlying stochastic processes. In particular, this implies that the insurance risk cannot be eliminated by increasing the size of the portfolio and appealing to the law of large numbers. We propose to apply techniques from incomplete markets in order to hedge and valuate these contracts. We consider a special case of the affine mortality structures considered by
Markowitz’s Mean–Variance Portfolio Selection with Regime Switching: A Continuous Time Model,
 SIAM J. Control Optim.
, 2003
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Markowitz revisited: meanvariance models in financial portfolio analysis
 SIAM Rev
, 2001
"... Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avo ..."
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Cited by 35 (1 self)
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Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.
Quadratic hedging and meanvariance portfolio selection with random parameters in an incomplete market
 Math. Opers. Res., Vol 29, No
, 2004
"... in an incomplete market ..."
Comparison of option prices in semimartingale models
 FINANCE STOCH
, 2006
"... In this paper we generalize recent comparison results of El Karoui, ..."
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Cited by 19 (5 self)
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In this paper we generalize recent comparison results of El Karoui,