We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem (infimum over market measures, supremum over the control) at each instance. Moreover, the underlying Bellman equations are intrinsically multi-dimensional. We propose a novel machine learning approach that solves for the local saddle-point at a chosen set of inputs and then uses a nonparametric (Gaussian process) regression to obtain a functional representation of the value function. Our algorithm resembles control randomization and regression Monte Carlo techniques but also brings multiple innovations, including adaptive experimental design, separate surrogates for optimal control and the local worst-case measure, and computational speed-ups for the sup-inf optimization. Thanks to the new scheme we are able to consider settings that have been previously computationally intractable and provide several new financial insights about learning and optimal trading under unknown market parameters. In particular, we demonstrate the financial advantages of adaptive robust framework compared to adaptive and static robust alternatives.

This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the artificial boundary method for solving the problem on a truncated domain, and derive several artificial boundary conditions (ABCs) on the artificial boundary of the bounded computational domain. A typical finite difference scheme and quadrature rule are used for the numerical solution of the reduced problem. Numerical experiments show that the proposed ABCs are able to improve the accuracy of the results and have a significant advantage over the widely-used boundary conditions by Heston in the original paper (Heston, 1993).

We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By following [28], we define the fundamental value $F$ of a risky asset $S$ as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [50]. We say that an asset price has a bubble if its fundamental value differs from the ask-price $(1+\lambda)S$. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.

Out of the companies, Dolby is the company with the best overall financial and operation health. According to the table that accounted its financial statements for the past three years, Dolby has stable profit margins that generates a revenue in the billions, the only company in ten figures.

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition between a stable regime for weak feedback to an unstable regime for strong feedback,in which liquidity crises arise with probability one. We characterize the critical exponents, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability.

We examine the novel problem of the estimation of transaction arrival processes in the intraday electricity markets. We model the inter-arrivals using multiple time-varying parametric densities based on the generalized F distribution estimated by maximum likelihood. We analyse both the in-sample characteristics and the probabilistic forecasting performance. In a rolling window forecasting study, we simulate many trajectories to evaluate the forecasts and gain significant insights into the model fit. The prediction accuracy is evaluated by a functional version of the MAE (mean absolute error), RMSE (root mean squared error) and CRPS (continuous ranked probability score) for the simulated count processes. This paper fills the gap in the literature regarding the intensity estimation of transaction arrivals and is a major contribution to the topic, yet leaves much of the field for further development. The study presented in this paper is conducted based on the German Intraday Continuous electricity market data, but this method can be easily applied to any other continuous intraday electricity market. For the German market, a specific generalized gamma distribution setup explains the overall behaviour significantly best, especially as the tail behaviour of the process is well covered.

Forecasting stock market direction is always an amazing but challenging problem in finance. Although many popular shallow computational methods (such as Backpropagation Network and Support Vector Machine) have extensively been proposed, most algorithms have not yet attained a desirable level of applicability. In this paper, we present a deep learning model with strong ability to generate high level feature representations for accurate financial prediction. Precisely, a stacked denoising autoencoder (SDAE) from deep learning is applied to predict the daily CSI 300 index, from Shanghai and Shenzhen Stock Exchanges in China. We use six evaluation criteria to evaluate its performance compared with the back propagation network, support vector machine. The experiment shows that the underlying financial model with deep machine technology has a significant advantage for the prediction of the CSI 300 index.

In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In real world voting scenarios, people often do not have complete information about other voter preferences and it can be computationally complex to identify a strategy that will maximize their expected utility. In such situations, it is often assumed that voters will vote truthfully rather than expending the effort to strategize. However, being truthful is just one possible heuristic that may be used. In this paper, we examine the effectiveness of heuristics in single winner and multi-winner approval voting scenarios with missing votes. In particular, we look at heuristics where a voter ignores information about other voting profiles and makes their decisions based solely on how much they like each candidate. In a behavioral experiment, we show that people vote truthfully in some situations and prioritize high utility candidates in others. We examine when these behaviors maximize expected utility and show how the structure of the voting environment affects both how well each heuristic performs and how humans employ these heuristics.

LSTMs promise much to financial time-series analysis, temporal and cross-sectional inference, but we find that they do not deliver in a real-world financial management task. We examine an alternative called Continual Learning (CL), a memory-augmented approach, which can provide transparent explanations, i.e. which memory did what and when. This work has implications for many financial applications including credit, time-varying fairness in decision making and more. We make three important new observations. Firstly, as well as being more explainable, time-series CL approaches outperform LSTMs as well as a simple sliding window learner using feed-forward neural networks (FFNN). Secondly, we show that CL based on a sliding window learner (FFNN) is more effective than CL based on a sequential learner (LSTM). Thirdly, we examine how real-world, time-series noise impacts several similarity approaches used in CL memory addressing. We provide these insights using an approach called Continual Learning Augmentation (CLA) tested on a complex real-world problem, emerging market equities investment decision making. CLA provides a test-bed as it can be based on different types of time-series learners, allowing testing of LSTM and FFNN learners side by side. CLA is also used to test several distance approaches used in a memory recall-gate: Euclidean distance (ED), dynamic time warping (DTW), auto-encoders (AE) and a novel hybrid approach, warp-AE. We find that ED under-performs DTW and AE but warp-AE shows the best overall performance in a real-world financial task.

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach. In the minimum-variance case, we prove that the analytical solution is significantly different from the one found numerically by Glasserman and Xu (2014) and that model risk reduces to an estimation risk. A detailed numerical example is provided.

The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987) and several of its extensions. Using perturbative arguments, we decompose the early exercise pricing problem into sub-problems of different orders and solve these sub-problems successively. The obtained solutions are combined to recover approximations to the original pricing problem of multiple orders, with the 0-th order version matching the general Barone-Adesi & Whaley ansatz. We test the accuracy and efficiency of the approximations via numerical simulations. The results show a clear dominance of higher order approximations over their respective 0-th order version and reveal that significantly more pricing accuracy can be obtained by relying on approximations of the first few orders. Additionally, they suggest that increasing the order of any approximation by one generally refines the pricing precision, however that this happens at the expense of greater computational costs.

Forests will have two notable economic roles in the future: providing renewable raw material and storing carbon to mitigate climate change. The pricing of forest carbon leads to longer rotation times and consequently larger carbon stocks, but also exposes landowners to a greater risk of forest damage. This paper investigates optimal forest rotation under carbon pricing and forest damage risk. I provide the optimality conditions for this problem and illustrate the setting with numerical calculations representing boreal forests under a range of carbon prices and damage probabilities. The relation between damage probability and carbon price towards the optimal rotation length is nearly linear, with carbon pricing having far greater impact. As such, increasing forest carbon stocks by lengthening rotations is an economically attractive method for climate change mitigation, despite the forest damage risk. Carbon pricing also increases land expectation value and reduces the economic risks of the landowner. The production possibility frontier under optimal rotation suggests that significantly larger forests carbon stocks are achievable, but imply lower harvests. However, forests' societally optimal role between these two activities is not yet clear-cut; but rests on the future development of relative prices between timber, carbon and other commodities dependent on land-use.

We consider a sequential social-learning environment with rational agents and Gaussian private signals, focusing on how the observation network affects the speed of learning. Agents learn about a binary state and take turns choosing actions based on own signals and network neighbors' behavior. The observation network generally presents an obstruction to the efficient rate of signal aggregation, as agents compromise between incorporating the signals of the observed neighbors and not over-counting the confounding signals of the unobserved early movers. We show that on any network, equilibrium actions are a log-linear function of observations and each agent's accuracy admits a signal-counting interpretation. Adding links to the observation network can harm agents even without introducing new confounds. We then consider a network structure where agents move in generations and observe all members of the previous generation. The additional information aggregated by each generation is asymptotically equivalent to fewer than two independent signals, even when generations are arbitrarily large.

The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential L\'evy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of the assets. Starting from an adaption of the continuous-time optional asset replacement problem initiated by McDonald and Siegel (1986), we derive tradeability premiums and subsequently characterize them in terms of free-boundary problems. This provides a simple way to compute non-tradeability values, e.g. by means of standard numerical techniques, and, in particular, to express the price of a non-tradeable asset as a percentage of the price of a tradeable equivalent. Our approach is illustrated via numerical examples where we discuss various properties of the tradeability premiums.