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991.
We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices. 相似文献
992.
993.
The stochastic integrals of M- type 2 Banach valued random functions w.r.t. compensated Poisson random measures introduced in (Rüdiger, B., 2004, In: Stoch. Stoch. Rep., 76, 213–242.) are discussed for general random functions. These are used to solve stochastic integral equations driven by non Gaussian Lévy noise on such spaces. Existence and uniqueness of the path wise solutions are proven under local Lipshitz conditions for the drift and noise coefficients on M-type 2 as well as general separable Banach spaces. The continuous dependence of the solution on the initial data as well as on the drift and noise coefficients are shown. The Markov properties for the solutions are analyzed. 相似文献
994.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):135-165
A class of Hilbert space-valued Markov processes which can be expressed as the mild solution of a linear abstract evolution equation is studied. Sufficient conditions for the generator of the Markov process to be well-defined are given and Kolmogorov's equation and an equation for the characteristic function of the process are derived. The theory is illustrated by examples of parabolic, hyperbolic and delay stochastic differential equations. 相似文献
995.
The paper deals with the pathwise uniqueness of solutions to one-dimensional time homogeneous stochastic differential equations with a diffusion coefficient σ satisfying the local time condition and measurable drift term b. We show that if the functions σ and b satisfy a non-degeneracy condition and fundamental solution to considered equation is unique in law, then pathwise uniqueness of solutions holds. Our result is in some sense negative, more precisely we give an example of an equation with Holder continuous diffusion coefficient and nondegenerate drift for which a fundamental solution is not unique in law and pathwise uniqueness of solutions does not hold. 相似文献
996.
997.
The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple. 相似文献
998.
研究了一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件,建立了两个振动定理,推广和改进了已有结果. 相似文献
999.
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum
hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance
equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance.
The proof is based on a priori estimates for the energy functional for a new observable constructed with an auxiliary function,
and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after
a finite time.
I.M. Gamba is supported by NSF-DMS0507038. M.P. Gualdani acknowledges partial support from the Deutsche Forschungsgemeinschaft,
grants JU359/5 and was partially supported under the Feodor Lynen Research fellowship. P. Zhang is partially supported by
the NSF of China under Grant 10525101 and 10421101, and the innovation grant from the Chinese Academy of Sciences. Part of
the work was done when P. Zhang visited the Department of Mathematics of Texas University at Austin, the author would like
to thank the hospitality of the department. Support from the Institute for Computational Engineering and Sciences at the University
of Texas at Austin is also gratefully acknowledged. 相似文献
1000.
D. Goreac 《Applied Mathematics and Optimization》2009,60(1):105-132
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system
with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the
dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded
operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability.
Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal
generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for
the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial
Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253–260, Chapman and
Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153–164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case. 相似文献