Related papers: Information Geometry of Risks and Returns
Herding, where investors imitate others' decisions rather than relying on their own analysis, is a prevalent phenomenon in financial markets. Excessive herding distorts rational decisions, amplifies volatility, and can be exploited by…
One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial…
Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant…
Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating…
We study the problem of hedging unit linked life insurance policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges:…
The recent crisis and the following flight to simplicity put most derivative businesses around the world under considerable pressure. We argue that the traditional modeling techniques must be extended to include product design. We propose a…
We consider a real options model for the optimal irreversible investment problem of a profit maximizing company. The company has the opportunity to invest into a production plant capable of producing two products, of which the prices follow…
This paper presents a theory of optimization fabrics, second-order differential equations that encode nominal behaviors on a space and can be used to define the behavior of a smooth optimizer. Optimization fabrics can encode commonalities…
Three types of geometric structure---grid triangulations, rectangular subdivisions, and orthogonal polyhedra---can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an…
Let X be a complex algebraic manifold of dimension n+1 embedded in a sufficiently higher dimensional complex projective space, and Y a generic hyperplane section of X. We describe the mixed Hodge structure on H^p(X-Y,C) and the Hodge…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities…
Many studies in economics deal with the non-reliability cost to assess insurance fees or investment analyses, but none takes into consideration the mechanical aspect of reliability analysis. Other studies in mechanics give some tools and…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…
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,…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function.…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
In this work, almost product and almost golden structures are studied. Conditions for those structures being Integrable and parallel are investigated. Also harmonicity of a map between almost pruduct or almost golden manifolds with pure or…