Lower bounds for densities of Asian type stochastic differential equations
Consider the following system of stochastic differential equations, \[ X^1_t = x^1 + \int_0^t \sigma(X_s)dW_s + \int_0^t b_1(X_s)ds, \quad X^2_t = x^2 + \int_0^t b_2(X_s)ds, \quad t \in [0,T]. \] They assume that \(\sigma,b_1,b_2\) are five times differentiable and have bounded derivatives but the functions themselves do not need to be bounded. The main goal of this paper is to give lower bounds for the density \(p_T(x,y)\) of \(X_T(x)\). These type of equations are linked to the so-called Asian option set-up as the authors claims.
scientific article; zbMATH DE number 5708601