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Confidence is central to safety and assurance cases: how much confidence a decision requires and how much the argument actually provides are both important questions. We present a new method for assessing probabilistic confidence in…
We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market,…
We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the…
We give a comprehensive review of credit term structure modeling methodologies. The conventional approach to modeling credit term structure is summarized and shown to be equivalent to a particular type of the reduced form credit risk model,…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
This paper studies nonparametric identification and counterfactual bounds for heterogeneous firms that can be ranked in terms of productivity. Our approach works when quantities and prices are latent, rendering standard approaches…
From the perspective of expectations of randomly stopped sums, Wald's equation and the Optional Sampling Theorem identify situations in which the stopping time can be decoupled from the stopping place, acting as if the two were independent.…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a…
We consider a conditional factor model for a multivariate portfolio of United States equities in the context of analysing a statistical arbitrage trading strategy. A state space framework underlies the factor model whereby asset returns are…
The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutative rings, in the direction of finite presentations, primary…
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
The recent banking crisis has again emphasized the importance of understanding and mitigating systemic risk in financial networks. In this paper, we study a market-driven approach to rescue a bank in distress based on the idea of claims…