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1.
Jose Manuel Corcuera Joao Guerra David Nualart Wim Schoutens 《Applied Mathematics and Optimization》2006,53(3):279-309
In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric
Levy process (taking into account jumps).
Except for the geometric Brownian model and the geometric Poissonian model, the
resulting models are incomplete and there are many equivalent martingale measures.
However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets
and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios
based in stocks
and bonds, showing that the new assets are superfluous for certain martingale measures
that depend on the utility function we use. 相似文献
2.
Summary In this paper we analize the reversibility of the diffusion property for the solution of certain infinite-dimensional systems of stochastic differential equations. Necessary and sufficient conditions ensuring this reversibility are given. The proofs use the techniques of the stochastic calculus of variations.This work was partly done when the first author was visiting the Centre de Recerca Matemàtica at Barcelona 相似文献
3.
Summary Consider a stochastic differential equation on
d
with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition. 相似文献
4.
In this paper we show that the local time of the Brownian motion belongs to the Sobolev space
for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to
, for any >0 and p>1 such that +1/p>1. 相似文献
5.
We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We also give a new proof of the main theorem in [D. Nualart, G. Peccati, Central limit theorems for sequences of multiple stochastic integrals, Ann. Probab. 33 (2005) 177–193] using techniques of Malliavin calculus. Finally, we extend our result to the multidimensional case and prove a weak convergence result for a sequence of square integrable random vectors, giving an application. 相似文献
6.
We introduce a notion of stochastic entropic solution à la Kruzkov, but with Ito's calculus replacing deterministic calculus. This results in a rich family of stochastic inequalities defining what we mean by a solution. A uniqueness theory is then developed following a stochastic generalization of L1 contraction estimate. An existence theory is also developed by adapting compensated compactness arguments to stochastic setting. We use approximating models of vanishing viscosity solution type for the construction. While the uniqueness result applies to any spatial dimensions, the existence result, in the absence of special structural assumptions, is restricted to one spatial dimension only. 相似文献
7.
A completely automated flow-injection system was developed for the monitoring of biosorption studies of Cu(II) ion on vegetable waste by-products. The system employed flow-through Cu(II)-selective electrodes, of epoxy-resin-CuS/Ag2S heterogeneous crystalline type, and computer controlled pumps and valves for the flow operation. Computer automation was done through a specially devised virtual instrument, which commanded and periodically calibrated the system, allowing for the monitoring of Cu(II) ions between 0.6 and 6530 mg L−1 at a typical frequency of 15 h−1. Grape stalk wastes were used as biosorbent to remove Cu(II) ions in a fixed-bed column with a sorption capacity of 5.46 mg g−1, obtained by the developed flow system, while the reference determination performed by FAAS technique supplied a comparable value of 5.41 mg g−1. 相似文献
8.
Summary In this work we study sigma fields and their tangent spaces on the Wiener space which are invariant in some sense with respect to the basic operators of the Malliavin Calculus. 相似文献
9.
10.
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus. 相似文献