We study a mathematical model capturing the support/resistance line method (a technique in technical analysis) where the underlying stock price transitions between two states of nature in a path-dependent manner. For optimal stopping problems with re
spect to a general class of reward functions and dynamics, using probabilistic methods, we show that the value function is $C^1$ and solves a general free boundary problem. Moreover, for a wide range of utilities, we prove that the best time to buy and sell the stock is obtained by solving free boundary problems corresponding to two linked optimal stopping problems. We use this to numerically compute optimal trading strategies for several types of dynamics and varying degrees of relative risk aversion. We then compare the strategies with the standard trading rule to investigate the viability of this form of technical analysis.
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model, and provides two linear approximations for the utility indifference price. The key tool is a probabilistic representation for the utility in
difference price by the solution of a functional differential equation, which is termed emph{pseudo linear pricing rule}. We also provide an alternative derivation of the quadratic BSDE representation for the utility indifference price.
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitt
ing method, whose convergence is proved based on the Barles-Souganidis monotone scheme, and the convergence rate is derived based on Krylovs shaking the coefficients technique. We apply our methodology to study the counterparty risk of derivatives in incomplete markets.
