6th NUS-USPC Workshop

18 – 19 Apr 2018, Singapore

PROGRAMME

Schedule for 18 Apr (Wed)
Schedule for 19 Apr (Thur)

ABSTRACTS

Wednesday, 18 April 2018
Time	Activity
09:00 – 09:30	Registration
09:30 – 09:40	Opening Address
09:40 – 10:25	Jean-François CHASSAGNEUX University Paris Diderot, France A Probabilistic Numerical Method for MFG
10:25 – 10:55	Group Photo cum Tea Break
10:55 – 11:40	Steven KOU National University of Singapore, Singapore Designing Stable Coins
11:40 – 12:25	Claudio FONTANA University Paris Diderot, France The Value of Informational Arbitrage
12:25 – 14:00	Lunch
14:00 – 14:45	Ilija ILIEVSKI National University of Singapore, Singapore Interpretable Forecasting of Financial Time Series with Deep Learning
14:45 – 15:30	Simon TRIMBORN National University of Singapore, Singapore Sparse-Group Network AutoRegressive Model for the Bitcoin Blockchain
15:30 – 16:00	Tea Break
16:00 – 16:45	Hao LEI National University of Singapore, Singapore Unsupervised Probabilistic Topic Modelling
16:45 – 17:30	Min DAI National University of Singapore, Singapore Robo-Advising: A Dynamic Mean-Variance Approach

Thursday, 19 April 2018
Time	Activity
09:00 – 09:30	Registration
09:30 – 10:30	Huyên PHAM University Paris Diderot, France Nicolas LANGRENE CSIRO, Australia Deep Learning Algorithms for Stochastic Control Problems
10:30 – 11:00	Tea Break
11:00 – 11:45	Michael KUPPER University of Konstanz, Germany Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks
11:45 – 12:30	Christa CUCHIERO University of Vienna, Austria Calibration Of Financial Models With Neural Networks
12:30 – 14:00	Lunch
14:00 – 15:00	Ivan GUO Monash University, Australia Gregoire LOEPER Monash University, Australia Machine Learning in Stochastic Optimal Transport and Volatility Calibration
15:00 – 15:15	Closing Address

Abstracts

A Probabilistic Numerical Method for MFG Jean-François CHASSAGNEUX, University Paris Diderot, France In this talk, I will first describe some problems in large population stochastic control (e.g. Mean-Field Games). The solution to these problems are characterised by a master equation, as observed by Lasry-Lions, which is a PDE written on the Wasserstein space of probability measure. I will recall the probabilistic representation of its solution in term of a (fully coupled) FBSDE with McKean-Vlasov interaction. I will then introduce a probabilistic scheme for this class of BSDEs and demonstrate its convergence both theoretically and practically. This is a joint work with D. CRISAN and F. DELARUE.

Calibration of Financial Models with Neural Networks Christa CUCHIERO, University of Vienna, Austria A central task in modeling, which has to be performed each day in banks and financial institutions, is to calibrate models to market and historical data. So far the choice which models should be used was not only driven by their capacity of capturing empirically observed market features well, but rather by computational tractability considerations. This is now undergoing a big change since neural net- work approaches offer the possibility to transform a daily online calibration into an offline learning phase and an online evaluation phase where the latter will be – thanks to the learning phase – extremely fast no matter what complex type of model needs to be calibrated. Inspired by the work of Andrez Hernandez [2], we consider two examples of calibration with neural networks: first a mixture model for interest rate dynamics in the spirit of [1] and second a local stochastic volatility model where the local volatility function is parametrized via neural nets. The is a joint work with Andres HERNANDEZ, Wahid KHOSRAWI and Josef TEICHMANN.

Robo-Advising: A Dynamic Mean-Variance Approach Min DAI, National University of Singapore, Singapore In contrast to the traditional financial advising, robo-advising needs to elicit investors’ risk profile via several simple online questions and to provide advice consistent with conventional investment wisdom, e.g. rich and young people should invest more in risky assets. We propose a dynamic portfolio choice model with the mean-variance criterion over portfolio log-returns that meets the two challenges. The model yields analytical and time-consistent optimal portfolio policies and can be used for robo-advising. This is a joint work with Hanqing JIN, Steven KOU and Yuhong Xu.

The Value of Informational Arbitrage Claudio FONTANA, University Paris Diderot, France In the context of a general semimartingale model of a complete market, we aim at answering the following question: How much is an investor willing to pay for learning some inside information that potentially allows to achieve arbitrage? If such a value exists, we call it the value of informational arbitrage. In particular, we are interested in the case where the inside information yields arbitrage opportunities but not unbounded profits with bounded risk. In the spirit of Amendinger et al. (2003), we provide a general answer to the above question by relying on an indifference valuation approach. To this effect, we establish some new results on models with inside information and study optimal investment-consumption problems in the presence of initial information and arbitrage, also allowing for the possibility of leverage. We characterize when the value of informational arbitrage is universal, in the sense that it does not depend on the preference structure. Our results are illustrated with several explicit examples.

Machine Learning in Stochastic Optimal Transport and Volatility Calibration Ivan GUO, Monash University, Australia Gregoire LOEPER, Monash University, Australia The landmark paper of Tan and Touzi studied a stochastic optimal transport problem which seeks a semimartingale diffusion process that matches known marginal densities at two different times. Duality results were established and a gradient-based numerical method was proposed to solve the dual problem. In the recent work of Guo, Loeper and Wang, stochastic optimal transport was applied to the problem of local volatility calibration. In particular, we seek a local volatility function that attains known marginal densities of the stock price (inferred from a continuum of vanilla option prices) at discrete maturities while minimising a cost function. The approach can also be modified to match a discrete set of option prices, thus eliminating the need for price interpolation. In this talk, we present a numerical approach to solve such stochastic optimal transport problems via neural networks. We take advantage of the fact that, for each randomly generated dual variable, the corresponding marginal density (or discrete option prices) can be easily solved via a Hamilton-Jacobi-Bellmen equation. These are then used to train a standard feed forward neural network to solve the inverse problem. The method can be further extended to the calibration of high-dimensional local stochastic volatility (LSV) models.

Interpretable Forecasting of Financial Time Series with Deep Learning Ilija ILIEVSKI, National University of Singapore, Singapore In this talk I will present our deep learning approach to forecasting financial multivariate time series which indicate the market sentiment towards a financial asset. The interpretable deep neural network reveals the essential dependence between the time series’ variables, and in contrast to the widely used vector autoregressive model, the deep learning model dynamically adapts the dependence coefficients to the ever-changing market conditions. Thus, the proposed method permits the study of the inter-variable relationships which yields a better understanding of the asset’s future price movements and consequently increases the profitability of the asset’s trading activities. I will conclude the talk with dependence analysis and forecasting performance for financial assets from different sectors and with vastly different market capitalisation.

Designing Stable Coins Steven KOU, National University of Singapore, Singapore Stable coins, which are cryptocurrencies pegged to other stable financial assets, are desirable for blockchain networks to be used as public accounting ledgers for payment transactions and as crypto money market accounts for asset allocation involving cryptocurrencies, whereby being often called the “Holy Grail of cryptocurrency.” However, existing cryptocurrencies, such as Bitcoins, are too volatile for these purposes. Inspired by the dual purpose funds popular in the US and China, we design, for the first time to our best knowledge, several dual-class structures that offer entitlements to either fixed income stable coins (class A funds) pegged to a traditional currency or leveraged investment opportunities (class B funds). Unlike traditional currencies, the new class A funds record all transactions on a blockchain, without centralized counterparties. By using the option pricing theory, we show that proposed stable coins indeed have very low volatility, similar to that of the short term U.S. treasury bonds. When combined with insurance from a government, the design can also serve a basis to issue a sovereign cryptocurrency. This is a joint work with Yizhou CAO, Min DAI, Lewei Li and Chen YANG.

Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks Michael KUPPER, University of Konstanz, Germany We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, and bounds on the distribution of a sum of dependent random variables. The talk is based on joint work with Stephan Eckstein.

Deep Learning Algorithms for Stochastic Control Problems Nicolas LANGRENE, CSIRO, Australia Huyên PHAM, University Paris Diderot, France We develop several deep learning-based algorithms for solving high-dimensional discrete-time stochastic control problems, which arise in the context of reinforcement learning or in the time-discretization of fully nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equations. Optimal state/action function (the so-called $Q$-function) from the Backward Bellman equation and policy functions are approximated by neural networks (NN) in the spirit of deep reinforcement learning. By relying on control randomization, NN approximation for $Q$-function are performed according to a regress now or a regress later Monte-Carlo approach joint with quantization, using value or performance iterations, and combined with the NN approximation of the policy function, either in a two-stage or in a simultaneous stochastic gradient descent. Our algorithms are illustrated and compared on various examples ranging from a HJB equation in high-dimension to option hedging and energy storage problems.

Unsupervised Probabilistic Topic Modelling Hao LEI, National University of Singapore, Singapore Probabilistic topic modeling is a way to extract the key information ‘topics’ from the unstructured text data. An extensively studied and popular model is the Latent Dirichlet Allocation (LDA). One of the unsolved problems in the field is to determine the number of topics. The usual approach is to try different numbers, for example, 10, 20, 30 etc, and compare their performance on the validation dataset. In this project, we propose a method to automatically find the ‘optimal’ number of topics as well as to select ‘significant’ features in each topic. We will implement our method to analyse financial news data comprised of 644,211 articles from 2006-04-02 to 2017-04-01.

Sparse-Group Network AutoRegressive Model for the Bitcoin Blockchain Simon TRIMBORN, National University of Singapore, Singapore Analyzing regional and size impact of bitcoin transactions is of great interest to understand the dynamic connection of the global cryptocurrency market. We propose a Sparse Group Network AutoRegressive (SGNAR) model to describe the essential dynamic dependence structure in the bitcoin market and to detect the active groups that have influential impact on the transaction flows in the global market. We develop the regularized least square estimator with both group and element sparsity assumption whereas group sparsity helps to highlight the regional effect and element sparsity implies the size impact of the active regions. In real data analysis, we found that the global network dynamic effects are coming from Europe and North America and only in the recent years, while the rising region Asia, though playing an important role in crypto mining, affects the transaction network weakly, and Africa is relatively independent.