Related papers: Possible mathematical formulation of liquidity pre…
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model, and provides two linear approximations for the utility indifference price. The key tool is a probabilistic representation for the…
An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables,…
This is a supplement to the paper "Liquidity based modeling of asset price bubbles via random matching". The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous…
In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…
Several models for the pricing of derivative securities in illiquid markets are discussed. A typical type of nonlinear partial differential equations arising from these investigation is studied. The scaling properties of these equations are…
With regard to the three basic states of matter (solid, liquid, gas), the calculation of the heat capacity of liquids in a general form has been considered one of the deepest and most interesting challenges in condensed matter physics, due…
We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility.…
A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so,…
Recent proposal for counterfactual computation [Hosten et al., Nature, 439, 949 (2006)] is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel…