arXiv · arXiv q-fin · 2016
This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It enables to recover the well-known results of Karatzas and Zhao in a fra…
Alexis Bismuth, Olivier Guéant, Jiang Pu
arXiv · arXiv q-fin · 2026
In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maximum risk) and lower variance (minimum risk). By introducing a risk factor $w$ to conduct coupled modeling of the maximum …
Jing He, Shuzhen Yang
arXiv · arXiv q-fin · 2016
We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trader director to provide better control on the trading rates. We formulate a stochastic control problem to determine the optimal dynamic strategy for trade execution, with a quadratic terminal pe…
Brian Bulthuis, Julio Concha, Tim Leung, Brian Ward
arXiv · arXiv · 2019
In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift…
Julian Hölzermann
arXiv · arXiv · 2013
Pricing extremely long-dated liabilities market consistently deals with the decline in liquidity of financial instruments on long maturities. The aim is to quantify the uncertainty of rates up to maturities of a century. We assume that the interest rates follow the affine mean-reverting Vasicek model. We model parameter uncertainty by Bayesian distributions over the parameters. The cross-sectional and time series par…
Anne Balter, Antoon Pelsser, Peter Schotman
arXiv · arXiv · 2026
Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that explicitly accounts for forecast uncertainty in volatility and covariance estimation to achieve empirical stability and reduced turnover, further improving other standard performance …
Adele Ravagnani, Mattia Chiappari, Andrea Flori, Piero Mazzarisi, Marco Patacca
arXiv · arXiv · 2025
This study develops an inverse portfolio optimization framework for recovering latent investor preferences including risk aversion, transaction cost sensitivity, and ESG orientation from observed portfolio allocations. Using controlled synthetic data, we assess the estimator's statistical properties such as consistency, coverage, and dynamic regret. The model integrates robust optimization and regret-based inference …
Jinho Cha, Long Pham, Thi Le Hoa Vo, Jaeyoung Cho, Jaejin Lee
arXiv · arXiv · 2018
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 a G-Brownian motion. The main question in this setting is how to find an arbitrage-free term structure. This question is crucial, since we can show that the classical approach, mar…
Julian Hölzermann
arXiv · arXiv · 2014
We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super-martingale under these measures. We also get the non-dominated optional decomposi…
Erhan Bayraktar, Zhou Zhou
arXiv · arXiv · 2026
Large language models (LLMs) are increasingly used as components of agentic systems that observe, plan, and act. In finance, even "assistive" systems become decision-relevant once their outputs are used to size trades or allocate risk. A key failure mode is the confidence--competence gap: a model that is only slightly better than chance but consistently overconfident will, under typical bet-sizing rules, generate neg…
Rishab Ghosh, Vinay Devarakonda
arXiv · arXiv · 2026
This paper examines how trade policy uncertainty influences the correlation between U.S. stock indices and short-term government bonds. The objective is to assess whether policy-related shocks, especially those linked to trade tensions, alter the traditional stock-T bill relationship and its implications for investors. We extend the Dynamic Conditional Correlation (DCC) framework by incorporating exogenous variables …
Demetrio Lacava
arXiv · arXiv · 2026
Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome \(Y\in\{0,1\}\) is inferred from an observed hist…
Juan Pablo Madrigal-Cianci, Camilo Monsalve Maya, Lachlan Breakey
arXiv · arXiv · 2025
We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential decision-making problem where the central bank observes macroeconomic conditions quarterly and chooses interest rate adjustments. Using publicly accessible historical Federal Reserve Econom…
Tony Wang, Kyle Feinstein, Sheryl Chen
arXiv · arXiv · 2025
A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility forecasting, fraud detection, and compliance monitoring. Our probabilistic, interpretable models deliver reliable results: We evaluate the performance of one-day-ahead 95% Value-at-Risk (V…
Sharif Al Mamun, Rakib Hossain, Md. Jobayer Rahman, Malay Kumar Devnath, Farhana Afroz
arXiv · arXiv · 2025
Conditional Autoencoders (CAEs) offer a flexible, interpretable approach for estimating latent asset-pricing factors from firm characteristics. However, existing studies usually limit the latent factor dimension to around K=5 due to concerns that larger K can degrade performance. To overcome this challenge, we propose a scalable framework that couples a high-dimensional CAE with an uncertainty-aware factor selection …
Ryan Engel, Yu Chen, Pawel Polak, Ioana Boier
arXiv · arXiv · 2025
This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for random returns without assuming any distribution. The model utilizes an uncertainty set grounded in a reproducing kerne…
Rupendra Yadav, Aparna Mehra
arXiv · arXiv · 2025
We present a novel framework for pricing waterfall structures by simulating the uncertainty of the cashflow generated by the underlying assets in terms of value, time, and confidence levels. Our approach incorporates various probability distributions calibrated on the market price of the tranches at inception. The framework is fully implemented in PyTorch, leveraging its computational efficiency and automatic differe…
Nicola Jean, Giacomo Le Pera, Lorenzo Giada, Claudio Nordio
arXiv · arXiv · 2024
We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but traditional methods based on second-moment shocks and time-varying volatility of the VIX often fail to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this,…
Ayush Jha, Abootaleb Shirvani, Svetlozar T. Rachev, Frank J. Fabozzi