A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study optimal investment under uncertain conditions.
New model for Knightian uncertainty with jumps.
Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are m…
A new method to break down insurance costs into risk and uncertainty.
We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors nor on the structure of the state space. Several aspects of modeling under Knightian Uncer…
We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of …
Paper recovers uncertainty from dynamic valuation rules.
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertain…
Investigates the effects of nondominated sets of probability measures in robust models of finance.
Set risk measures extend traditional risk measures to handle sets of positions.
We show that, under mild assumptions, some unimaginable events - which we refer to as Black Swan events - must necessarily occur. It follows as a corollary of our theorem that any computational model of decision-making under uncertainty is incomplete in the sense that not all events that occur can be taken into account…
The paper addresses pricing interest rate derivatives in markets with volatility uncertainty.
We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity averse decision maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends on either a linear combination of the factors or the radial part of the driving…
We give explicit solutions for utility maximization of terminal wealth problem in the presence of Knightian uncertainty in continuous time in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space o…
The target of this paper is to consider model the risky asset price on the financial market under the Knightian uncertainty, and pricing the ask and bid prices of the uncertain risk. We use the nonlinear analysis tool, i.e., G-frame work [26], to construct the model of the risky asset price and bid-ask pricing for the …
Foundation for robust finance using rough path theory.
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability. In this survey paper, we review some of these developments and point to some ar…
Study path-dependent affine models under uncertain parameters for financial applications.
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying t…
Paper establishes robust no-arbitrage conditions under projective determinacy.
Study on inventory management under uncertainty using smooth ambiguity preference.
Study vector-valued robust control under uncertainty.
We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of …
The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On th…
The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider …
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping time problems are investig…
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…
In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative investment rules over a given time horizon, and under any admissible configurati…
We propose a method to assess the intrinsic risk carried by a financial position when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces th…
Pari-mutuel markets are trading platforms through which the common market maker simultaneously clears multiple contingent claims markets. This market has several distinctive properties that began attracting the attention of the financial industry in the 2000s. For example, the platform aggregates liquidity from the ind…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number …
Unified method for input, data, and model uncertainty in neural networks.
This paper benchmarks uncertainty disentanglement across various tasks.
Unified Bayesian framework for quantifying GNN uncertainty.
Proposes a new criterion for reliable uncertainty estimation in deep neural networks.
Proposes a method to quantify uncertainty in graph neural networks for node classification.
Survey on uncertainty in ML and DL, covering sources, quantification, and decision-making.
Unified Uncertainty Calibration improves AI predictions by combining different types of uncertainty.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
Paper decomposes risk into aleatoric and epistemic uncertainties and generates predictive uncertainty measures.
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to distributional mismatch between the test and training data distributions. Differe…
New method estimates model uncertainty in regression.
Introduces hierarchical uncertainty using U-sequences.
Connects robust optimization to conformal prediction for uncertainty sets.
We propose orthogonality as a necessary condition for disentangling aleatoric and epistemic uncertainty.
This work introduces a method to decompose uncertainty in in-context learning for large language models.
Cooperative model disentangles data uncertainties.
Framework disentangles deep feature uncertainty for efficient inference.