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In this paper, we discuss the evolution of the optical beam in nonlocal cubic nonlinear media, modeled by the nonlocal nonlinear Schrödinger equation (NNLSE). A different approximate model to the NNLSE is presented for the strongly nonlocal media with arbitrary response functions. An exact analytical solution of the model is obtained, and a spatial soliton… (More)

- Min Dai, Lishang Jiang, Peifan Li, Fahuai Yi
- SIAM J. Control and Optimization
- 2009

This paper concerns continuous-time optimal investment and consumption decision of a CRRA investor who faces proportional transaction costs and finite time horizon. In the no consumption case, it has been studied by Liu and Loewenstein (2002) and Dai and Yi (2006). Mathematically, it is a singular stochastic control problem whose value function satisfies a… (More)

- Fahuai Yi, Zhou Yang, Xiaohua Wang
- SIAM J. Math. Analysis
- 2008

- Fahuai Yi
- 2008

Abstract: In this paper we consider a parabolic variational inequality arising from the valuation of European installment put options. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually we show its numerical result by the binomial method.

- Huiwen Yan, Fahuai Yi
- 2011

The model of pricing American-style convertible bond is formulated as a zero-sum Dynkin game, which can be transformed into a parabolic variational inequality PVI . The fundamental variable in this model is the stock price of the firm which issued the bond, and the differential operator in PVI is linear. The optimal call and conversion strategies correspond… (More)

- Xiaoshan Chen, Fahuai Yi
- SIAM J. Control and Optimization
- 2012

- Fahuai Yi, T. M. Shih
- Applied Mathematics and Computation
- 1998

This paper deals with the equation @1H
u r~vH
u ÿ ru f in D0
XT ; where X is a bounded domain in R
n P 2 with @X 2 C; and XT X
0; T : H is a maximal monotonic graph and ~v : XT ! R is a known smooth vector function. We prove the existence of weak solution, uniqueness and obtain an error estimate for the approximating process. Ó 1998 Elsevier… (More)

- Zuo Quan Xu, Fahuai Yi
- 2015

A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion fluctuations. The consumption rate is subject to an upper bound constraint which linearly depends on the investor’s wealth… (More)

- Fahuai Yi, Yingshan Chen
- Applied Mathematics and Computation
- 2008

- FAHUAI YI, JINDUO LIU
- 2016

In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat e goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space… (More)