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Martingale Schrödinger bridges and optimal semistatic portfolios
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called...
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Variance-Minimal Hedging
This chapter is devoted to the determination of optimal hedging strategies by the criterion of variance-minimal strategies. In incomplete market...
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A martingale method for option pricing under a CEV-based fast-varying fractional stochastic volatility model
Modeling the volatility smile and skew has been an active area of research in mathematical finance. This article proposes a hybrid stochastic–local...
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Utility Optimization, Minimum Distance Martingale Measures, and Utility Indifference Pricing
This chapter gives an introduction to the determination (resp. selection) of option prices via minimum distance martingales as well as to pricing and...
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Winding of geodesic rays chosen by a harmonic measure
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain...
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Existence and Uniqueness of Martingale Solutions to Option Pricing Equations with Noise
We introduce a new option pricing equation with noise in a frictional financial market, which is fully different from the classical option pricing...
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Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows
We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend on measure flows. We...
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On an aggregate state-price deflator in a multi-period market model
In this paper, we study arbitrage theory in a basic multi-period market model. Malamud and Trubowitz (Math Financ Econ 1(2): 129–161, 2007) used an...
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Martingales and Path Decompositions
In this chapter, we use the Perron–Frobenius decomposition of the NBP to show the existence of an intrinsic family of martingales. These are...
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Improved robust price bounds for multi-asset derivatives under market-implied dependence information
We show how inter-asset dependence information derived from market prices of options can lead to improved model-free price bounds for multi-asset...
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On Locally Concave Functions on Simplest Nonconvex Domains
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about...
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Highness properties close to PA completeness
Suppose we are given a computably enumerable object. We are interested in the strength of oracles that can compute an object that approximates this...
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Optimal Stop** of Geometric Markov Renewal Chains and Pricing
This chapter presents an optimal stop** problem for geometric Markov renewal chains and pricing in financial mathematics for American and European...
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