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作者：Soner, H. M.; Shreve, S. E.; Cvitanic, J.
作者单位：Carnegie Mellon University
摘要：Conventional wisdom holds that since continuous-time, Black-Scholes hedging is infinitely expensive in a model with proportional transaction costs, there is no continuous-time strategy which hedges a European call option perfectly. Of course, if one is attempting to dominate the European call rather than replicate it, then one can use the trivial strategy of buying one share of the underlying stock and holding to maturity. In this paper we prove that this is, in fact, the least expensive metho...
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作者：Duffie, Darrell; Ma, Jin; Yong, Jiongmin
作者单位：Stanford University; Purdue University System; Purdue University; Fudan University
摘要：This paper confirms a version of a conjecture by Fischer Black regarding consol rate models for the term structure of interest rates. A consol rate model is one in which the stochastic behavior of the short rate is influenced by the consol rate. Since the consol rate is itself determined, via the usual discounted present value formula, by the short rate, such models have an inherent fixed point aspect. Under an equivalent martingale measure, purely technical regularity conditions are given for...
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作者：Kaspi, Haya; Mandelbaum, Avi
作者单位：Technion Israel Institute of Technology
摘要：Levy bandits are multi-armed bandits driven by Levy processes. As anticipated from existing research, Levy bandits are optimally controlled by an index strategy: One can associate with each arm an index function of its state, and optimal strategies are those that allocate time to arms whose states have the largest index. Furthermore, the index function of an arm is calculated independently of the other arms, and the optimal reward can be expressed in terms of the indices. Somewhat less anticip...
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作者：Ritter, Klaus; Wasilkowski, Grzegorz W.; Wozniakowski, Henryk
作者单位：University of Erlangen Nuremberg; University of Kentucky; Columbia University
摘要：We present sharp bounds on the minimal errors of linear estimators for multivariate integration and L-2-approximation. This is done for a random field whose covariance kernel is a tensor product of one-dimensional kernels that satisfy the Sacks-Ylvisaker regularity conditions.
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作者：Dempster, M. A. H.; Ye, J. J.
作者单位：University of Essex; Dalhousie University; University of Victoria
摘要：This paper concerns the optimal impulse control of piecewise deterministic Markov processes (PDPs). The PDP optimal (full) control problem with dynamic control plus impulse control is transformed to an equivalent dynamic control problem. The existence of an optimal full control and a generalized Bellman-Hamilton-Jacobi necessary and sufficient optimality condition for the PDP full control problem in terms of the value function for the new dynamic control problem are derived. It is shown that t...
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作者：Roberts, G. O.; Shortland, C. F.
作者单位：University of Cambridge
摘要：We consider the problem of estimating first exit distributions for one-dimensional diffusion processes. We provide analytic bounds and an approximation which is shown to be accurate in a range of numerical examples involving Brownian motion.
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作者：Dassios, Angelos
作者单位：University of London; London School Economics & Political Science
摘要：The study of the quantile of a Brownian motion with a drift is undertaken. An explicit formula for its density, as well as a representation of its distribution as the sum of the maximum and the minimum of two resealed independent Brownian motions with drift, is given. The result is used in the pricing of a financial path-dependent option due to Miura.
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作者：Funaki, T.; Surgailis, D.; Woyczynski, W. A.
作者单位：Nagoya University; Vilnius University; University System of Ohio; Case Western Reserve University; University System of Ohio; Case Western Reserve University
摘要：We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the bumps. In certain cases, this work extends an earlier effort by Surgailis and Woyczynski, where only noninteracting bumps driven by the traditional doubly stochastic Poisson process were considered. In con...
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作者：Kallianpur, G.; Xiong, J.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Tennessee System; University of Tennessee Knoxville
摘要：Under suitable conditions, it is proved that limits of sequences of nuclear space-valued solutions of stochastic differential equations driven by Poisson random measures are characterized by diffusion equations. The results are applied to models of environmental pollution and to reversal potential models of neuronal behavior.
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作者：Akahori, Jiro
作者单位：University of Tokyo
摘要：In this paper we present an explicit form of the distribution function of the occupation time of a Brownian motion with a constant drift (if there is no drift, this is the well-known arc-sine law). We also define the alpha-percentile of the stock price and give an explicit form of the distribution function of this random variable. Using this explicit distribution, we calculate the price of a new type of path-dependent option, called the alpha-percentile option. This option was first introduced...
