This chapter discusses computational methods for approximating portfolio and asset pricing problems. Formulation of these problems is usually specified along with components, preferences, payoffs, etc., that are analytic functions. This implies that the solutions to these problems acquire this...

The analytic method of Chen, Cosimano, and Himonas (CCH 2009) is extended to prove that the continuous time version of the long run risk model of Bansal and Yaron (2004) has an analytic solution. The long run risk model is dependent on the recursive utility introduced by Duffie and Epstein...

For risk management, implementing risk measures and backtesting them are essential tasks. Since the expected shortfall (ES) possesses coherence and tail sensitivity, the Basel Committee has raised the option to replace the classical risk measure value-at-risk (VaR) with ES. However, the...