Large deviations and exact asymptotics for perpetuities with small discount rates

Large Deviations and Exact Asymptotics for Constrained Exponential Random Graphs

Refined large deviations asymptotics for Markov-modulated infinite-server systems

Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers’ arrival rates and service rates are modulated by a Markovian background process; additionally, there are infinitely many servers (and consequently the resulting model is often used as a proxy for the corresponding many-server model). The Markov-modulated infinite-server mo...

Approximations for the Distribution of Perpetuities with Small Discount Rates

General perpetuities (i.e. random variables of the formD = R∞ 0 e −Γ(t−)dΛ (t), also known as infinite horizon discounted rewards) play an important role in several application settings (e.g. insurance, finance and time series analysis). Our focus is on developing approximations for the distribution of D that are asymptotically valid when the “accumulated short rate process” or “accumulated for...

Investment hysteresis under stochastic interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However for many decisions, revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of I...

Asymptotics of Forward Implied Volatility

We study asymptotics of forward-start option prices and the forward implied volatility smile using the theory of sharp large deviations (and refinements). In Chapter 1 we give some intuition and insight into forward volatility and provide motivation for the study of forward smile asymptotics. We numerically analyse no-arbitrage bounds for the forward smile given calibration to the marginal dist...