排序方式: 共有33条查询结果,搜索用时 31 毫秒
1.
Framstad N. C. Øksendal B. Sulem A. 《Journal of Optimization Theory and Applications》2004,121(1):77-98
We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting and show the connections of adjoint processes to dynamic programming. The result is applied to financial optimization problems. 相似文献
2.
Bernt Øksendal 《Inventiones Mathematicae》1988,91(2):273-297
Summary Given a quasiregular function on an open setU in
n
it is shown that there exists a diffusionX
t inU such that mapsX
t inton-dimensional Brownian motion. The process is constructed from a Dirichlet form which can be described explicitly. This enables us to apply stochastic methods in the investigation of quasiregular mappings. Some examples of applications are given, including boundary behaviour and value distribution. 相似文献
3.
We use white noise calculus and the Donsker Delta Function to find explicit formulas for the replicating portfolios in a Black–Scholes market for a class of contingent T-claims. 相似文献
4.
The purpose of this paper is to present a general stochastic calculus
approach to insider trading. We consider a market driven by a standard Brownian
motion $B(t)$ on a filtered probability space $\displaystyle
(\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are
adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$,
with $\F_t\subset\G_t$ for all $t\in [0,T]$, $T>0$ being a fixed terminal time.
By
an {\it insider} in this market we
mean a person who has access to a filtration (information)
$\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly
bigger than the filtration
$\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$.
In this context an insider strategy is represented by an
$\H_t$-adapted process
$\phi(t)$ and we interpret all anticipating integrals as
the forward integral defined in
[23] and [25].
We consider an optimal portfolio problem with
general utility for an insider with access to a general information
$\H_t \supset\G_t$ and show that if
an optimal insider portfolio $\pi^*(t)$ of this problem exists, then
$B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement
of filtration property holds. This is a converse of previously
known results in this field.
Moreover, if $\pi^*$ exists
we obtain an explicit expression in terms of $\pi^*$ for the
semimartingale decomposition of $B(t)$ with respect to $\H_t$.
This is a generalization
of results in [16], [20] and [2]. 相似文献
5.
Francesca Biagini Yaozhong Hu Bernt
ksendal Agns Sulem 《Stochastic Processes and their Applications》2002,100(1-2):233-253
We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formwhere B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter
. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion. 相似文献
dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),
6.
7.
Bernt Øksendal 《Journal of Functional Analysis》1976,22(3):283-294
Suppose Γ is a simple closed C2 curve in the complex plane and let W1, W2 be the components of the complement of Γ. Let X be a compact plane set. Necessary and sufficient conditions are given that any two points x1?X ∩ W1, and x2?X ∩ W2 belong to different Gleason parts for the algebra R(X). We also give an answer to the question: How thin can a nontrivial part for R(X) be ? 相似文献
8.
9.
Admissible investment strategies in continuous trading 总被引:3,自引:0,他引:3
We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy. 相似文献
10.
Helge Holden Tom Lindstrøm Bernt Øksendal Jan Ubøe Tu-Sheng Zhang 《Probability Theory and Related Fields》1993,95(3):391-419
Summary We give a program for solving stochastic boundary value problems involving functionals of (multiparameter) white noise. As an example we solve the stochastic Schrödinger equation {ie391-1} whereV is a positive, noisy potential. We represent the potentialV by a white noise functional and interpret the product of the two distribution valued processesV andu as a Wick productV u. Such an interpretation is in accordance with the usual interpretation of a white noise product in ordinary stochastic differential equations. The solutionu will not be a generalized white noise functional but can be represented as anL
1 functional process. 相似文献