| Summary: | The objective of this thesis is to contribute in the understanding of both the induced
behavior and the underlying risks of a decision maker who is rewarded through option-like
compensation schemes or who is subject to risk tolerance constraints.
In the first part of the thesis we consider a risk averse investor who maximizes his
expected utility subject to a risk tolerance constraint expressed in terms of the risk measure
known as Conditional Value-at-Risk. We study some of the implicit risks associated with the
optimal strategies followed by this investor. In particular, embedded probability measures
are uncovered using duality theory and used to assess the probability of surpassing a loss
threshold defined by the risk measure known as Value-at-Risk. Using one of these embedded
probabilities, we derive a measure of the financial cost of hedging the loss exposure associated
to the optimal strategies, and we show that, under certain assumptions, it is a coherent
measure of risk.
In the second part of the thesis, we analyze the investment decisions that managers
undertake when they are paid with option-like compensation packages. We consider two
particular cases:
• We study the optimal risk taking strategies followed by a fund manager who is paid
through a relatively general option-like compensation scheme. Our analysis is developed
in a continuous-time framework that permits to obtain explicit formulas. These
are used first to analyze the incentives induced by this type of compensation schemes
and, second, to establish criterions to determine appropriate parameter values for these
compensation packages in order to induce specific manager's behaviors.
• We consider a hedge fund manager who is paid through a simple option-like compensation
scheme and whose investment universe includes options. We analyze the nature of the optimal investment strategies followed by this manager. In particular, we establish
explicit optimal conditions for option investments in terms of embedded martingale
measures that are derived using duality theory. Our analysis in this case is developed
in a discrete-time framework, which allows to consider incomplete markets and fat-tailed
distributions -such as option return distributions- in a much simpler manner
than in a continuous-time framework. === Business, Sauder School of === Graduate
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