Superreplication under model uncertainty in discrete time

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a suitable Banach space. The main ingredient is a closedness result for the set of claims which can be superreplicated from zero capital; its proof relies on medial limits.     

International stock return predictability under model uncertainty

This paper examines return predictability when the investor is uncertain about the right state variables. A novel feature of the model averaging approach used in this paper is to account for finite-sample bias of the coefficients in the predictive regressions. Drawing on an extensive international dataset, we find that interest-rate related variables are usually among the most prominent predictive variables, whereas valuation ratios perform rather poorly. Yet, predictability of market excess returns weakens substantially, once model uncertainty is accounted for. We document notable differences in the degree of in-sample and out-of-sample predictability across different stock markets. Overall, these findings suggest that return predictability is neither a uniform, nor a universal feature across international capital markets.     

Monetary policy under model and data-parameter uncertainty

Empirical Taylor rules are much less aggressive than those derived from optimization-based models. This paper analyzes whether accounting for uncertainty across competing models and (or) real-time data considerations can explain this discrepancy. It considers a central bank that chooses a Taylor rule in a framework that allows for an aversion to the second-order risk associated with facing multiple models and measurement-error configurations. The paper finds that if the central bank cares strongly enough about stabilizing the output gap, this aversion leads to significant declines in the coefficients of the Taylor rule even if the central bank's loss function assigns little weight to reducing interest rate variability. Furthermore, a small degree of aversion can generate an optimal rule that matches the empirical Taylor rule.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

Forecasting exchange rates under parameter and model uncertainty

We introduce a forecasting method that closely matches the econometric properties required by exchange rate theory. Our approach formally models (i) when (and if) predictor variables enter or leave a regression model, (ii) the degree of parameter instability, (iii) the (potentially) rapidly changing relevance of regressors, and (iv) the appropriate shrinkage intensity over time. We consider (short-term) forecasting of six major US dollar exchange rates using a standard set of macro fundamentals. Our results indicate the importance of shrinkage and flexible model selection/averaging criteria to avoid poor forecasting results.     

The market price of fiscal uncertainty

Recent fiscal interventions have raised concerns about US public debt, future distortionary tax pressure, and long-run growth potential. We explore the long-run implications of public financing policies aimed at short-run stabilization when: (i) agents are sensitive to model uncertainty, as in Hansen and Sargent (2007), and (ii) growth is endogenous, as in Romer (1990). We find that countercyclical deficit policies promoting short-run stabilization reduce the price of model uncertainty at the cost of significantly increasing the amount of long-run risk. Ultimately these tax policies depress innovation and long-run growth and may produce welfare losses.     

Hedging decisions with price and output uncertainty

We generally show that the introduction of output uncertainty does not affect the hedging position of the firm.     

Energy price uncertainty and the value premium

This paper examines the impact of energy price uncertainty on a range of value anomalies. We demonstrate that the value premium is substantially stronger in periods of heightened energy price uncertainty. Energy price uncertainty exerts an asymmetric effect on the value anomalies, whereby downside energy price uncertainty accentuates the return differences between value and growth stocks compared to upside energy uncertainty. These findings are consistent with the argument that value firms possess a larger amount of inflexible assets than growth firms. Therefore, they struggle more to adjust in periods of elevated energy price uncertainty. We also demonstrate that energy price uncertainty has predictive power on the value premium one-month ahead. Using the Feasible Generalized Least Squares predictive model, energy price uncertainty can help mean-variance investors to obtain a positive annual utility gain across the value anomalies for up to 16.71%.     

Economic policy uncertainty and stock price crash risk

We examine the impact of economic policy uncertainty (EPU) on firm-specific crash risk. Based on a large sample of Chinese listed firms over the period from 2000 to 2017, we provide empirical evidence that firms are more likely to experience stock price crashes when EPU increases. Cross-sectionally analysis further reveals that the impact of EPU on stock price crash risk is stronger for firms whose returns are more sensitive to EPU. More specifically, young stocks, small stocks, high volatility stocks, and growth stocks, which have higher valuation uncertainty per se, are more sensitive to EPU and are more affected by EPU in terms of crash risk. We further show that EPU is significantly and positively associated with aggregated stock price crash risk at the market level.     

Gold price dynamics and the role of uncertainty

This study focuses on the dynamics of the gold price against bonds, stocks and exchange rates based on a disaggregation of the underlying relationships across different frequencies applying a wavelet decomposition. To analyze joint extreme movements (i.e. tail dependence), we adopt a copula approach, which helps us to assess the dependence between the returns of gold and other assets in calm and turmoil market times and therefore the hedge and safe haven functions of gold. We also examine whether gold prices are directly affected by changes in macroeconomic uncertainty, economic policy uncertainty and/or CPI forecasters disagreement. Analyzing data for nine economies for a sample period starting in 1985, we find that the role of gold changes significantly after the collapse of Lehman Brothers in 2008. Gold is unable to serve as a hedge or safe haven in the classical sense while the findings for the period prior to 2008 mostly suggest that gold is able to shield investors. Uncertainty measures display a surprising and time-varying relationship with the path of the gold price. While economic policy uncertainty is positively correlated with gold price changes, macroeconomic uncertainty and inflation uncertainty among forecasters are both negatively related to gold price changes.     

Economic policy uncertainty and stock price crash risk

This paper studies the impact of economic policy uncertainty on stock price crash risk using data from China. We develop a new index to measure Chinese economic policy uncertainty and find that economic policy uncertainty has a remarkable positive effect on stock price crash risk. However, the effect reverses later. The results also indicate that the positive effect of economic policy uncertainty on stock price crash risk is more prominent for state‐owned enterprises. Moreover, this effect is more prominent for firms with higher information asymmetry and firms with greater disagreement among investors, indicating that economic policy uncertainty affects crash risk through two mechanisms: managers’ concealment of bad news and investors’ heterogeneous beliefs.     

Strategy under uncertainty

At the heart of the traditional approach to strategy lies the assumption that by applying a set of powerful analytic tools, executives can predict the future of any business accurately enough to allow them to choose a clear strategic direction. But what happens when the environment is so uncertain that no amount of analysis will allow us to predict the future? What makes for a good strategy in highly uncertain business environments? The authors, consultants at McKinsey & Company, argue that uncertainty requires a new way of thinking about strategy. All too often, they say, executives take a binary view: either they underestimate uncertainty to come up with the forecasts required by their companies' planning or capital-budging processes, or they overestimate it, abandon all analysis, and go with their gut instinct. The authors outline a new approach that begins by making a crucial distinction among four discrete levels of uncertainty that any company might face. They then explain how a set of generic strategies--shaping the market, adapting to it, or reserving the right to play at a later time--can be used in each of the four levels. And they illustrate how these strategies can be implemented through a combination of three basic types of actions: big bets, options, and no-regrets moves. The framework can help managers determine which analytic tools can inform decision making under uncertainty--and which cannot. At a broader level, it offers executives a discipline for thinking rigorously and systematically about uncertainty and its implications for strategy.     

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and ?itkovi? (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk \(\hat{\lambda}\) and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with \(\hat{\lambda}\) and with the leverage being proportional to the investor’s confidence in her estimate.     

A generalized probability framework to model economic agents' decisions under uncertainty

The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance have produced valuable results. The principal movement which has steered this research direction is known under the name of ‘econophysics’. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under ‘uncertainty’ in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as ‘quantum probability’) enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.     

Oil price uncertainty and stock price informativeness: Evidence from investment-price sensitivity in China

We study the effects of oil price uncertainty (OPU) on stock price informativeness based on investment-price sensitivity. Using Chinese stocks from 2008 to 2021, we find a negative relationship between OPU and the strength of Tobin's q (a standardized measure of prices) for predicting investment opportunities. This finding is likely due to the crowding out of informed investors rather than the financial constraints brought by a higher cost of capital. Investment-price sensitivity also decreases more among firms in less-competition, high sales volatility, and lower analysts' attention. What is more, the reduction in investment-price sensitivity is more concentrated in public utilities, agriculture & livestock, and industry instead of in real estate or commerce industries. These findings indicate that OPU decreases the acquisition of information related to firms, and consequently, price informativeness for future investment decisions.     

Informed trading,information uncertainty,and price momentum

In this paper we investigate the effects of informed trading (PIN) and information uncertainty in determining price momentum. We find that trading strategies based on buying high-uncertainty good-news stocks and shorting high-uncertainty bad-news stocks work well when limited to high-PIN stocks, while stocks with low-PIN do not exhibit price continuations, even when the uncertainty level of those stocks is high. In contrast, momentum returns are always significant for high-PIN stocks, irrespective of information uncertainty. Overall, we show that the informed trading effect is both independent of and stronger than that of information uncertainty in determining price momentum.     

A model of optimal portfolio selection under liquidity risk and price impact

We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to a solvency constraint. This is formulated as an impulse control problem under state constraints and we characterize the value function as the unique constrained viscosity solution to the associated quasi-variational Hamilton–Jacobi–Bellman inequality. We would like to thank Mihail Zervos for useful discussions.     

Optimal stopping under model uncertainty and the regularity of lower Snell envelopes

The analysis of American options in incomplete markets has motivated the development of robust versions of the classical Snell envelopes: The cost of superhedging an American option is characterized by the upper Snell envelope, while the infimum of the arbitrage prices is given by the lower Snell envelope. Lower Snell envelopes also appear in the problem of optimal stopping under model uncertainty. In this paper we focus on the lower Snell envelope. We construct a regular version of this stochastic process. To this end, we apply results due to Dellacherie and Lenglart on the regularization of stochastic processes and 𝒯-Systems.