Using a suitable change of probability measure, we obtain a Poisson series representation for the arbitrage‐free price process of vulnerable contingent claims in a regime‐switching market driven by an underlying continuous‐time Markov process. As a result of this representation, along with a short‐time asymptotic expansion of the claim’s price process, we develop an efficient novel method for pricing claims whose payoffs may depend on the full path of the underlying Markov chain. The proposed...

Dynamic capital structure models with roll‐over debt rely on widely accepted arguments that have never been formalized. This paper clarifies the literature and provides a rigorous formulation of the equity holders’ decision problem within a game theory framework. We spell out the linkage between default policies in a rational expectations equilibrium and optimal stopping theory. We prove that there exists a unique equilibrium in constant barrier strategies, which coincides with that derived in...

The paper is concerned with the first and the second fundamental theorems of asset pricing in the case of nonexploding financial markets, in which the excess‐returns from risky securities represent continuous semimartingales with absolutely continuous predictable characteristics. For such markets, the notions of “arbitrage” and “completeness” are characterized as properties of the distribution law of the excess‐returns. It is shown that any form of arbitrage is tantamount to guaranteed...

We introduce a new stochastic control framework where in addition to controlling the local coefficients of a jump‐diffusion process, it is also possible to control the intensity of switching from one state of the environment to the other. Building upon this framework, we develop a large investor model for optimal consumption and investment that generalizes the regime‐switching approach of Bäuerle and Rieder (2004).

We present an alternative approach to the pricing of bonds and bond derivatives in a multivariate factor model for the term structure of interest rates that is based on the solution of an optimal stochastic control problem. It can also be seen as an alternative to the classical approach of computing forward prices by forward measures and as such can be extended to other situations where traditionally a change of measure is involved based on a change of numeraire. We finally provide explicit...

We consider a portfolio optimization problem in a defaultable market with finitely‐many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. By separating the utility maximization problem into a predefault and postdefault component, we deduce two coupled...

We generalize Merton’s asset valuation approach to systems of multiple financial firms where cross‐ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no‐arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no‐arbitrage prices are provided. A result on...

We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power‐law and exponential‐decay order book models explicitly and discuss several extensions. We also consider the...

We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are nonnegative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable martingales with respect to their own forward measure. Additionally, and most importantly, our approach also leads to analytically tractable expressions of multi‐LIBOR payoffs. This approach unifies therefore...

We study shortfall risk minimization for American options with path‐dependent payoffs under proportional transaction costs in the Black–Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time BS model, for a given initial capital, there exists a portfolio strategy which minimizes the shortfall risk. In the absence of transactions costs (complete markets) similar limit...