In this paper an arbitrage strategy is constructed for the modified Black–Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock...

Given that the terminal condition is of at most linear growth, it is well known that a Cauchy problem admits a unique classical solution when the coefficient multiplying the second derivative (i.e., the volatility) is also a function of at most linear growth. In this note, we give a condition on...

In this paper we examine a consistency problem for a multi-factor jump diffusion model. First we bridge a gap between a jump-diffusion model and a generalized Heath-Jarrow-Morton (HJM) model, and bring a multi- factor jump-diffusion model into the HJM framework. By applying the drift condition...

Given an Heath-Jarrow-Morton (HJM) interest rate model and a parametrized family of finite dimensional forward rate curves, this paper provides us a way to project this infinite dimensional HJM forward rate curve to the finite dimensional manifold. This projection characterizes banks' behavior...

Given a Heath–Jarrow–Morton (HJM) interest rate model $\mathcal{M}$ and a parametrized family of finite dimensional forward rate curves $\mathcal{G}$, this paper provides a technique for projecting the infinite dimensional forward rate curve rt given by $\mathcal{M}$ onto the finite...

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to include stochastic volatility in the risky asset's price...

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an...

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the...

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate...

Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and...