We develop a new method to find the number of volatility regimes in a non-stationary financial time series. We use change point detection to partition a time series into locally stationary segments, then estimate the distributions of each piece. The distributions are clustered into a learned number of discrete volatility regimes via an optimisation routine. Using this method, we investigate and determine a clustering structure for indices, large cap equities and exchange-traded funds. Finally, we create and validate a dynamic portfolio allocation strategy that learns the optimal match between the current distribution of a time series with its past regimes, thereby making online risk-avoidance decisions in the present.

This paper establishes a new decomposition of optimal dynamic portfolio choice under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy from market incompleteness and flexible wealth-dependent utilities. We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly time-varying interest rate, we solve in closed-form the HARA policy as a combination of a bond holding scheme and a corresponding CRRA strategy. Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive.

We employ both random forests and LSTM networks (more precisely CuDNNLSTM) as training methodologies to analyze their effectiveness in forecasting out-of-sample directional movements of constituent stocks of the S&P 500 from January 1993 till December 2018 for intraday trading. We introduce a multi-feature setting consisting not only of the returns with respect to the closing prices, but also with respect to the opening prices and intraday returns. As trading strategy, we use Krauss et al. (2017) and Fischer & Krauss (2018) as benchmark and, on each trading day, buy the 10 stocks with the highest probability and sell short the 10 stocks with the lowest probability to outperform the market in terms of intraday returns -- all with equal monetary weight. Our empirical results show that the multi-feature setting provides a daily return, prior to transaction costs, of 0.64% using LSTM networks, and 0.54% using random forests. Hence we outperform the single-feature setting in Fischer & Krauss (2018) and Krauss et al. (2017) consisting only of the daily returns with respect to the closing prices, having corresponding daily returns of 0.41% and of 0.39% with respect to LSTM and random forests, respectively.

We propose a highly schematic economic model in which, in some cases, wage inequalities lead to higher overall social welfare. This is due to the fact that high earners can consume low productivity, non essential products, which allows everybody to remain employed even when the productivity of essential goods is high and producing them does not require everybody to work. We derive a relation between heterogeneities in technologies and the minimum Gini coefficient required to maximize global welfare. Stronger inequalities appear to be economically unjustified. Our model may shed light on the role of non-essential goods in the economy, a topical issue when thinking about the post-Covid-19 world.

Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in practice it varies. How do traders come to learn these parameters? We introduce natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders. We prove convergence of these opinion dynamics using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.

In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the underlying problem is constructed as a limit of dyadic impulse strategies by exploiting regularity properties of the linked risk sensitive optimal stopping value functions. In particular, this shows that the discretized setting could be used to approximate near optimal strategies for the underlying continuous time control problem, which facilitates the usage of the standard approximation tools. For completeness, we present examples of processes that could be embedded into our framework.

This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially controllable by the agent as healthcare reduces mortality growth. To the best of our knowledge, this is the first time Epstein-Zin utilities are formulated on a controllable random horizon, via an infinite-horizon backward stochastic differential equation with superlinear growth. A new comparison result is established for the uniqueness of associated utility value processes. In a Black-Scholes market, the stochastic control problem is solved through the related Hamilton-Jacobi-Bellman (HJB) equation. The verification argument features a delicate containment of the growth of the controlled morality process, which is unique to our framework, relying on a combination of probabilistic arguments and analysis of the HJB equation. In contrast to prior work under time-separable utilities, Epstein-Zin preferences largely facilitate calibration. In four countries we examined, the model-generated mortality closely approximates actual mortality data; moreover, the calibrated efficacy of healthcare is in broad agreement with empirical studies on healthcare across countries.

Attempts to allocate capital across a selection of different investments are often hampered by the fact that investors' decisions are made under limited information (no historical return data) and during an extremely limited timeframe. Nevertheless, in some cases, rational investors with a certain level of experience are able to ordinally rank investment alternatives through relative assessments of the probabilities that investments will be successful. However, to apply traditional portfolio optimization models, analysts must use historical (or simulated/expected) return data as the basis for their calculations. This paper develops an alternative portfolio optimization framework that is able to handle this kind of information (given by an ordinal ranking of investment alternatives) and to calculate an optimal capital allocation based on a Cobb-Douglas function, which we call the Sorted Weighted Portfolio (SWP). Considering risk-neutral investors, we show that the results of this portfolio optimization model usually outperform the output generated by the (intuitive) Equally Weighted Portfolio (EWP) of different investment alternatives, which is the result of optimization when one is unable to incorporate additional data (the ordinal ranking of the alternatives). To further extend this work, we show that our model can also address risk-averse investors to capture correlation effects.

It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination which has been proposed in the literature by including business (intrinsic, market) time. We define a mixed Levy subordinated model by adding a single subordinated Levy process to the well-known log-normal model, resulting in a new log-price process. We apply the proposed models to study the behavioral finance notion of "greed and fear" disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. We then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Our result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders.

The 2008 mortgage crisis is an example of an extreme event. Extreme value theory tries to estimate such tail risks. Modern finance practitioners prefer Expected Shortfall based risk metrics (which capture tail risk) over traditional approaches like volatility or even Value-at-Risk. This paper provides a quantum annealing algorithm in QUBO form for a dynamic asset allocation problem using expected shortfall constraint. It was motivated by the need to refine the current quantum algorithms for Markowitz type problems which are academically interesting but not useful for practitioners. The algorithm is dynamic and the risk target emerges naturally from the market volatility. Moreover, it avoids complicated statistics like generalized pareto distribution. It translates the problem into qubit form suitable for implementation by a quantum annealer like D-Wave. Such QUBO algorithms are expected to be solved faster using quantum annealing systems than any classical algorithm using classical computer (but yet to be demonstrated at scale).

In this paper we derive semi-closed form prices of barrier (perhaps, time-dependent) options for the Hull-White model, ie., where the underlying follows a time-dependent OU process with a mean-reverting drift. Our approach is similar to that in (Carr and Itkin, 2020) where the method of generalized integral transform is applied to pricing barrier options in the time-dependent OU model, but extends it to an infinite domain (which is an unsolved problem yet). Alternatively, we use the method of heat potentials for solving the same problems. By semi-closed solution we mean that first, we need to solve numerically a linear Volterra equation of the first kind, and then the option price is represented as a one-dimensional integral. Our analysis shows that computationally our method is more efficient than the backward and even forward finite difference methods (if one uses them to solve those problems), while providing better accuracy and stability.

Successfully combating climate change will require substantial technological improvements in Low-Carbon Energy Technologies (LCETs). An efficient allocation of R&D budgets to accelerate technological advancement necessitates a better understanding of how LCETs rely on scientific knowledge. In this paper, we sketch for the first time the evolution of knowledge bases for key LCETs and show how technological interdependencies change in time. We use data covering almost all US patents as well as scientific articles published in the past two centuries to quantify the history of LCETs and their dependence on science. We show how the drivers of low-carbon innovations shifted from Hydro and Wind energy to Nuclear fission, and more recently to Solar PV and back to Wind. Our analysis demonstrates that 1) LCETs rely increasingly on science, 2) Solar PV and Nuclear fusion depend heavily on science, while Hydro energy does not, 3) renewable and nuclear energy technologies rely on a strikingly different kind of science, and 4) there is a remarkable convergence of scientific knowledge bases of renewables over recent decades. These findings suggest a need for technology-specific research policies, although targeted research in renewables is likely to cross-fertilize a wider range of LCETs.