We prove the existence and uniqueness of solutions to a class quadratic backward SDE (BSDE) systems which we call triangular quadratic. Our results generalize several existing about diagonally BSDEs in non-Markovian setting. As part our analysis, obtain new linear with unbounded coefficients, may be independent interest. Through nonuniqueness example, answer “crucial open question” raised by Ha...

in this paper, we extend some famous maximal inequalities and obtain strong laws of largenumbers for arbitrary random variables by use of these inequalities and martingale techniques.

In this paper, we will establish a martingale inequality, which extends the classic Hoeffding inequality in some sense. In addition, our inequality improves the results of Lee and Su [7] (2002) in some cases.

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingal...

In an incomplete financial market in which the dynamics of the asset prices is driven by a d-dimensional continuous semimartingale X, we consider the problem of pricing European contingent claims embedded in a power utility framework. This problem reduces to identifying the p-optimal martingale measure, which can be given in terms of the solution to a semimartingale backward equation. We use th...

(x) when u(0, x) is the cumulative distribution function of a signed measure on IR. We associate a nonlinear martingale problem with the Fokker-Planck equation obtained by spatial differentiation of the conservation law. After checking uniqueness for both the conservation law and the martingale problem, we prove existence thanks to a propagation of chaos result for systems of interacting partic...

We show that a càdlàg, local martingale has conditionally independent increments and symmetric jumps if and only if its law is invariant under integral transformations which preserve quadratic variation.