We discuss a concept denoted as Conformal Prediction (CP) in this paper. While initially stemming from the world of machine learning, it was never applied or analyzed in the context of short-term electricity price forecasting. Therefore, we elaborate the aspects that render Conformal Prediction worthwhile to know and explain why its simple yet very efficient idea has worked in other fields of application and why its characteristics are promising for short-term power applications as well. We compare its performance with different state-of-the-art electricity price forecasting models such as quantile regression averaging (QRA) in an empirical out-of-sample study for three short-term electricity time series. We combine Conformal Prediction with various underlying point forecast models to demonstrate its versatility and behavior under changing conditions. Our findings suggest that Conformal Prediction yields sharp and reliable prediction intervals in short-term power markets. We further inspect the effect each of Conformal Prediction's model components has and provide a path-based guideline on how to find the best CP model for each market.

Stock prediction is a topic undergoing intense study for many years. Finance experts and mathematicians have been working on a way to predict the future stock price so as to decide to buy the stock or sell it to make profit. Stock experts or economists, usually analyze on the previous stock values using technical indicators, sentiment analysis etc to predict the future stock price. In recent years, many researches have extensively used machine learning for predicting the stock behaviour. In this paper we propose data driven deep learning approach to predict the future stock value with the previous price with the feature extraction property of convolutional neural network and to use Neural Arithmetic Logic Units with it.

This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.

Uber and Lyft ride-hailing marketplaces use dynamic pricing, often called surge, to balance the supply of available drivers with the demand for rides. We study pricing mechanisms for such marketplaces from the perspective of drivers, presenting the theoretical foundation that has informed the design of Uber's new additive driver surge mechanism. We present a dynamic stochastic model to capture the impact of surge pricing on driver earnings and their strategies to maximize such earnings. In this setting, some time periods (surge) are more valuable than others (non-surge), and so trips of different time lengths vary in the opportunity cost they impose on drivers. First, we show that multiplicative surge, historically the standard on ride-hailing platforms, is not incentive compatible in a dynamic setting. We then propose a structured, incentive-compatible pricing mechanism. This closed-form mechanism has a simple form, and is well-approximated by Uber's new additive surge mechanism.

The effects of weather on agriculture in recent years have become a major concern across the globe. Hence, the need for an effective weather risk management tool (weather derivatives) for agricultural stakeholders. However, most of these stakeholders are unwilling to pay for the price of weather derivatives (WD) because of product-design and geographical basis risks in the pricing models of WD. Using machine learning ensemble technique for crop yield forecasting and feature importance, the major major weather variable (average temperature) that affects crop yields are empirically determined. This variable (average temperature) is used as the underlying index for WD to eliminate product-design basis risks. A model with time-varying speed of mean reversion, seasonal mean, local volatility that depends on the average temperature and time for the contract period is proposed. Based on this model, pricing models for futures, options on futures, and basket futures for cumulative average temperature and growing degree-days are presented. Pricing futures on baskets reduces geographical basis risk as buyer's have the opportunity to select the most appropriate weather stations with their desired weight preference. With these pricing models, agricultural stakeholders can hedge their crops against the perils of weather.

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of dynamic discrete choice models under such economically motivated exclusion restrictions on primitive utilities. We show that each exclusion restriction leads to an easily interpretable moment condition with the discount factor as the only unknown parameter. The identified set of discount factors that solves this condition is finite, but not necessarily a singleton. Consequently, in contrast to common intuition, an exclusion restriction does not in general give point identification. Finally, we show that exclusion restrictions have nontrivial empirical content: The implied moment conditions impose restrictions on choices that are absent from the unconstrained model.

Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence--Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if $\mu_{0}$ is atomless, but not in general. In the one-period case $n=1$, these transports reduce to the Left-Curtain coupling of Beiglb\"ock and Juillet. In the multiperiod case, the bivariate marginals for dates $(0,t)$ are of Left-Curtain type, if and only if $\mu_{0},\dots,\mu_{n}$ have a specific order property. The general analysis of the transport problem also gives rise to a strong duality result and a description of its polar sets. Finally, we study a variant where the intermediate marginals $\mu_{1},\dots,\mu_{n-1}$ are not prescribed.

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

This paper studies the finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markovian regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving an innovative martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent but simplified form. This allows us to connect the previous control problem to a quadratic BSDE with jumps that is new to the literature, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some novel truncation techniques, we obtain the existence of solution to this new BSDE using the delicate convergence of solutions associated to some truncated BSDEs. The verification theorem and the characterization of the optimal trading strategy can be concluded with the aid of our newly established BSDE results.

Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we propose a Deviation-based approach to quantify uncertainty. Furthermore, the theory is illustrated with a practical case study from NASDAQ index.

Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements to compute the Sharpe ratio, namely, the expected returns and the volatilities are unknown numbers and need to be estimated statistically. This means that the Sharpe ratio used by funds is likely to be error prone because of statistical estimation errors. In this paper, we provide various tests to measure the quality of the Sharpe ratios. By quality, we are aiming at measuring whether a manager was indeed lucky of skillful. The test assesses this through the statistical significance of the Sharpe ratio. We not only look at the traditional Sharpe ratio but also compute a modified Sharpe insensitive to used Capital. We provide various statistical tests that can be used to precisely quantify the fact that the Sharpe is statistically significant. We illustrate in particular the number of trades for a given Sharpe level that provides statistical significance as well as the impact of auto-correlation by providing reference tables that provides the minimum required Sharpe ratio for a given time period and correlation. We also provide for a Sharpe ratio of 0.5, 1.0, 1.5 and 2.0 the skill percentage given the auto-correlation level.

The 2008 financial crisis has been attributed to "excessive complexity" of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of clearing a financial network after a shock. Prior work has shown that when banks can only enter into simple debt contracts with each other, then this problem can be solved in polynomial time. In contrast, if they can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank, a solution may not even exist.

In this work, we show that deciding if a solution exists is NP-complete if CDSs are allowed. This remains true if we relax the problem to $\varepsilon$-approximate solutions, for a constant $\varepsilon$. We further show that, under sufficient conditions where a solution is guaranteed to exist, the approximate search problem is PPAD-complete for constant $\varepsilon$. We then try to isolate the "origin" of the complexity. It turns out that already determining which banks default is hard. Further, we show that the complexity is not driven by the dependence of counterparties on each other, but rather hinges on the presence of so-called naked CDSs. If naked CDSs are not present, we receive a simple polynomial-time algorithm. Our results are of practical importance for regulators' stress tests and regulatory policy.