Related papers: Information Geometry of Risks and Returns
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In modern recommender systems, both users and items are associated with rich side information, which can help understand users and items. Such information is typically heterogeneous and can be roughly categorized into flat and hierarchical…
This paper addresses the trade-off between internalisation and externalisation in the management of stochastic trade flows. We consider agents who must absorb flows and manage risk by deciding whether to warehouse it or hedge in the market,…
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry…
In this work we present the results of several simulations on main-effect factorial designs. The goal of such simulations is to investigate the connections between the $D$-optimality of a design and its geometrical structure. By means of a…
This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…
Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable…
Previous studies into the budget constraint of portfolio optimization problems based on statistical mechanical informatics have not considered that the purchase cost per unit of each asset is distinct. Moreover, the fact that the optimal…
We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving…
In this paper, we study the optimal investment problem considering the herd behaviour between two agents, including one leading expert and one following agent whose decisions are influenced by those of the leading expert. In the objective…
Observation of the workings of productive organizations shows that the characteristics of a trade, backed by nature given to a technological environment, determine the productive combination implemented by the decision maker, and the…
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
Framework materials and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into polynomial constraints, making algebraic geometry…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
We study optimal bundling when consumers differ in one dimension. We introduce a partial order on the set of bundles defined by (i) set inclusion and (ii) sales volumes (if sold alone and priced optimally). We show that if the undominated…
In algebraic geometry there is the notion of a height pairing of algebraic cycles, which lies at the confluence of arithmetic, Hodge theory and topology. After explaining a motivating example situation, we introduce new directions in this…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…