This research offers a way to hedge earthquake risks within a Japanese stock and fixed income portfolio of an investment bank and better understand Japanese markets. It goes beyond the Basel approaches and discusses the necessity of using more sophisticated risk measures than the Value-at-Risk and how to optimize these measures in modern portfolio theory. The "Otemachi-Approach" is introduced as the process on how to decide to optimize ones portfolio from a risk manager's view and which measures of risk are appropriate within a fast moving environment, i.e. financial markets. It compares a variety of approaches of portfolio theory to find the most appropriate one for banks in a daily reporting scheme. The approach revealed that by diversifying ones portfolio by adding/demanding earthquake technology related firms (seismic isolators) and gum as a commodity to the portfolio. We were able to debunk the idea of hedging by investments in the construction industry by back-testing Japanese market moves. It offers a step-by-step guide to abstract a very specific problem of Japanese markets to a general risk management problem in the financial industry, i.e. portfolio optimization and measuring risk. For better understanding of modern portfolio theory we find examples that outline the necessity of using coherent risk measures in practice. By using a so-called extremal representation of CVaR, we reformulate the optimal control problem as a bilevel optimization problem in which the outer optimization problem is convex and the inner optimization problem is standard stochastic optimal control. We were able to reduce the amount of historical data to optimize Expected Shortfall of a portfolio and we were able to lose restrictions of Miller's model by using a Record to Record algorithm. We also proposed to additionally use the Wasserstein metric to measure the quality of approximated CVaR as received from the model.