Related papers: Hedging under generalized good-deal bounds and mod…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We consider model-free pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
A quantum field theory generalization, Baaquie, of the Heath, Jarrow, and Morton (HJM) term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
We study the Hull-White model for the term structure of interest rates in the presence of volatility uncertainty. The uncertainty about the volatility is represented by a set of beliefs, which naturally leads to a sublinear expectation and…
We introduce a two-agent problem which is inspired by price asymmetry arising from funding difference. When two parties have different funding rates, the two parties deduce different fair prices for derivative contracts even under the same…
We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of…
This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a…
Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered.…
We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case…
We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any…
In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…
This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded…
This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We examine the effect of different market…