The major contribution of the three essays is extending microeconomic theory within the area of financial asset replacement under evolving stochastic costs and revenue. Each of the three assays offers unique extensions. The first essay, chapter 2, considers a virgin technology as opposed to initiating an investment from an idle project. The theory is more complex but is of a more general framework by allowing replacement of a virgin technology. This advancement is within the framework of integrating game theoretical models into real options analysis with uncertain arrival of mature technology emerging in the future. The unique contribution within this framework is considering multiple stochastic processes modeled by correlated geometric Brownian motions. The theoretical results reveal the replacement criteria consisting of option values, hurdle rates, first-mover advantages, threats by rivals and technical uncertainties. Our extension reveals how the conventional real option theory should be modified to consider firm interactions and uncertain arrival time of advanced technologies. The existence of early adopters of a technology earning monopoly rents and such rents being mitigated by late adopters and adjusting options values associated with future available technology enriches out understanding of asset replacement. The second essay, chapter 3, considers the idea of slippage in cofire adoption when there is an energy loss in cofiring relative to coal firing. The larger the slippage, the less likely cofiring will replace coal. This aids in developing the theoretical link between CO2 allowance price and the price premium for biomass. The percentage of biomass to coal is theoretically positively related to the ratio of allowance price and price premium. If a policy dictates proportion of biomass, then the allowance price should be set at a higher rate than the price premium. However, policy should be considered in the context of possible increased slippage. When to replacement a virgin coal plant which is operated in a competitive market and what should the replacement be (cofiring coal with biomass or solar) is the topic of essay three, chapter 4. Both a current solar technology, technology I, and a future not yet available solar technology, technology II, are considered. Economic theory is extended by considering an operational project as opposed to initiating from an idle project. This involves developing a theoretical model, which employs multiple compound options to model a renewable transition. In a period of transition from fossil fuels to renewables, extending the economic theory that addresses the major benefits and costs of this transition is vital in revealing the correct path forward. Our theory and applications indicate this abandonment of transition to renewables does not necessarily have to occur. Cofiring coal with biomass may offer a path, which provides a bridge to future availability of renewables. By extending the life of virgin coal plants with cofiring the correct transition path forward may be achieved.