This chapter introduces basic concepts of modern finance theory and demonstrates how to apply them in complex real-world problems. Financial deals and investment decisions are typically determined under uncertainty.Therefore, although this chapter is self-contained, we have to expect some theoretical background in individual decisionmaking and optimal investment under uncertainty. We organize our discussion into four central sections. The starting point is a portfolio choice problem, where an investor has to choose between different assets with specific risk and return characteristics. We then move on to some option pricing applications. We first derive analytical formulas and then evaluate numerical procedures for pricing European and American options as well as more exotic option products. The third section elaborates on credit risk measurement and management using a corporate bond portfolio as example. In the last section we discuss mortality risk and the optimal portfolio structure of a life insurance company. This section provides different numerical approaches to find an optimal portfolio structure with many risky assets. It begins with simple measures of risk and return of a single asset and then develops decision rules to choose optimal portfolios that maximize expected utility of wealth in worlds without and with riskless borrowing and lending opportunities. The purpose of this section is to optimize a portfolio of equity shares and a risk-free investment opportunity. The investor faces the most basic two-period investment choice problem: He buys assets in the first period and these assets pay off in the next period. The problem of the investor is to choose from i = 1, . . . ,N risky assets which may be shares, bonds, real estate, etc. The gross return of each asset i is denoted by rit = qit/qit−1 − 1, where qit−1 is the first-period market price and qit − qit−1 the second-period payoff.
An optimal portfolio, consumption-leisure and retirement choice problem with CES utility: a dynamic programming approach
