In the past decade a lot of attention has been devoted to the option valuation approach to i~vestments in financial economics. This theory provides a fl exible way of incorporating uncertainty and irreversibility into the making of the investment decision. The primary purpose of this study is to extend the contingent claim approach by introducing a strategic dimension into the investment decision. In particular we focus on the case where an investor may be preempted by one or more competitors, and where there is an advantage of acting first. Secondly, we apply the strategic options approach to some important areas in financial economics, such as corporate investment under uncertainty, corporate default , market micro-structure . and the timing of arbitrage. Apart from illustrating the wide applicability and relevance of the techniques, this also clarifies some important issues in financial economics. 'Option Games' (jointly written with William Perraudin) describes a way of incorporating strategic behaviour and asymmetric information into optimal stopping decisions under uncertainty. vVe derive optimal stopping rules when each agent's payoff is affected by the actions of other agents and these latter are of unknown type. 'Strategic Sequential Investments: an Application to Preemptive Patenting' derives the optimal investment rules for an incumbent and a challenger who both have an option to patent an innovation with stochastic payoff. We find that the optimal trigger rule is determined by a trade-off between the benefit of waiting to invest and the need to act quickly due to the competitive threat. In particular, we demonstrate that both the strategic Marshallian break-even investment trigger and the trigger obtained by the option valuation approach are in fact limit_ing polar cases of the strategic investment trigger developed in this paper. We then extend the model to a two-stage sequential investment situation where the first and the second stage respectively consist of patenting and launching the product. The model allows us to explain and analyse the phenomenon of sleeping patents. It appears that sleeping patents are more likely to occur when interest rates are low, price volatility is high or when the first stage_ cost is small relative to the second stage cost. 'Creditor Races and Contingent Claims' (jointly written with William Perraudin) presents a simple pricing model in which two debt-holders with incomplete information about each other's type decide when to foreclose on a financially-distressed firm. 'The Timing of Arbitrage: an Options Approach' presents a continuous-time modei for the timing of riskless arbitrage when the mispricing between two equivalent portfolios varies stochastically through time under the exogenous impact of liquidity trades and when there is a persistent prospect that the arbitrage bubble can 'burst'. The model endows the arbitrageur with n options to do arbitrage. When endogenously determined arbitrage bounds a re violated one or more arbitrage trades bring asset prices back within the bounds. The model is extended to the case where there are two competing arbitrageurs who have incomplete information about each other's type.