Bitcoin, as one of the most popular cryptocurrency, is recently attracting much attention of investors. Bitcoin price prediction task is consequently a rising academic topic for providing valuable insights and suggestions. Existing bitcoin prediction works mostly base on trivial feature engineering, that manually designs features or factors from multiple areas, including Bticoin Blockchain information, finance and social media sentiments. The feature engineering not only requires much human effort, but the effectiveness of the intuitively designed features can not be guaranteed. In this paper, we aim to mining the abundant patterns encoded in bitcoin transactions, and propose k-order transaction graph to reveal patterns under different scope. We propose the transaction graph based feature to automatically encode the patterns. A novel prediction method is proposed to accept the features and make price prediction, which can take advantage from particular patterns from different history period. The results of comparison experiments demonstrate that the proposed method outperforms the most recent state-of-art methods.

This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation setting, based on a theoretical hedging framework discussed in existing literature. We look at hedging CVA market risk for a portfolio with European options on a stock, first in a Black-Scholes setting, then in a Merton jump-diffusion setting. Furthermore, we analyze the trading business at a bank after including xVAs in pricing. We provide insights into the hedging of derivatives and their xVAs by analyzing and visualizing the cash-flows of a portfolio from a desk structure perspective. The case study shows that not charging CVA at trade inception results in an expected loss. Furthermore, hedging CVA market risk is crucial to end up with a stable trading strategy. In the Black-Scholes setting this can be done using the underlying stock, whereas in the Merton jump-diffusion setting we need to add extra options to the hedge portfolio to properly hedge the jump risk. In addition to the simulation, we derive analytical results that explain our observations from the numerical experiments. Understanding the hedging of CVA helps to deal with xVAs in a practical setting.

We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be guaranteed that only one of the rates affects pricing, linear equations can be recovered and analytical formulae can be derived. Moreover, as a byproduct, our results explain how debt value adjustment (DVA) and funding benefits are dissimilar. It is often believed that considering both DVA and funding benefits results in a double-counting issue but it will be shown that the two components are affected by different mathematical structures of derivative transactions. We find that funding benefit is related to the decreasing property of the payoff function, but this relationship decreases as the funding choices of underlying assets are transferred to repo markets.

Recently, some transportation service providers attempt to integrate the ride services offered by multiple independent ride-sourcing platforms, and passengers are able to request ride through such third-party integrators or connectors and receive service from any one of the platforms. This novel business model, termed as third-party platform-integration in this paper, has potentials to alleviate the cost of market fragmentation due to the demand splitting among multiple platforms. While most existing studies focus on the operation strategies for one single monopolist platform, much less is known about the competition and platform-integration as well as the implications on operation strategy and system efficiency. In this paper, we propose mathematical models to describe the ride-sourcing market with multiple competing platforms and compare system performance metrics between two market scenarios, i.e., with and without platform-integration, at Nash equilibrium as well as social optimum. We find that platform-integration can increase total realized demand and social welfare at both Nash equilibrium and social optimum, but may not necessarily generate a greater profit when vehicle supply is sufficiently large or/and market is too fragmented. We show that the market with platform-integration generally achieves greater social welfare. On one hand, the integrator in platform-integration is able to generate a thicker market and reduce matching frictions; on the other hand, multiple platforms are still competing by independently setting their prices, which help to mitigate monopoly mark-up as in the monopoly market.

Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the underlying asset, we allow for the disclosure of future information about the terminal price of the asset by modeling it as a Brownian bridge. This model may be used under special market conditions, in particular we focus on what in the literature is known as the "pinning effect", that is, when the price of the asset approaches the strike price of a highly-traded option close to its expiration date. Our main mathematical contribution is in characterizing the solution to the optimal stopping problem when the gain function includes the discount factor. We show how to numerically compute the solution and we analyze the effect of the volatility estimation on the strategy by computing the confidence curves around the optimal stopping boundary. Finally, we compare our method with the optimal exercise time based on a geometric Brownian motion by using real data exhibiting pinning.

We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to:

--Write arbitrage as curvature of a principal fibre bundle.

--Parameterize arbitrage strategies by its holonomy.

--Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization.

--Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance.

--Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where:

-->Arbitrage is allowed but minimized.

-->Arbitrage is not allowed.

--Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition. The converse is in general not true and additionally requires the Novikov condition for the instantaneous Sharpe Ratio Dynamics to be satisfied.

We investigate a group choice problem of agents pursuing social status. We assume heterogeneous agents want to signal their private information (ability, income, patience, altruism, etc.) to others, facing tradeoff between "outside status" (desire to be perceived in prestigious group from outside observers) and "inside status" (desire to be perceived talented from peers inside their group). To analyze the tradeoff, we develop two stage signaling model in which each agent firstly chooses her group and secondly chooses her action in the group she chose. They face binary choice problems both in group and action choices. Using cutoff strategy, we construct an partially separating equilibrium such that there are four populations: (i) choosing high group with strong incentive for action in the group, (ii) high group with weak incentive, (iii) low group with strong incentive, and (iv) low group with weak incentive. By comparative statics results, we find some spillover effects from a certain group to another, on how four populations change, when a policy is taken in each group. These results have rich implications for group choice problems like school, firm or residential preference.

National culture is among those societal factors which could influence research and innovation activities. In this study, we investigated the associations of two national culture models with citation impact of nations (measured by the proportion of papers belonging to the 10% and 1% most cited papers in the corresponding fields, PPtop 10% and PPtop 1%). Bivariate statistical analyses showed that of six Hofstede's national culture dimensions (HNCD), three dimensions of power distance, individualism, and uncertainty avoidance had statistically significant associations with citation impact of nations. The study also revealed that of two Inglehart-Welzel cultural values (IWCV), the value survival versus self-expression is statistically significantly related to citation impact indicators. We additionally calculated multiple regression analyses controlling for the possible effects of confounding factors including international migrant stock, investments in research and development, number of researchers, international co-authorships, and national self-citations. The results revealed that the statistically significant associations of HNCD with citation impact indicators disappeared. But the statistically significant relationship between survivals versus self-expression values and citation impact indicators remained stable even after controlling for the confounding variables. Thus, the freedom of expression and trust in society might contribute to better scholarly communication systems, higher level of international collaborations, and further quality research.

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited samples. A key difficulty that limits the widespread practical use of these optimization formulations is the large amount of data required by the state-of-the-art sample average approximation schemes to approximate the CVaR objective with high fidelity. Unlike the state-of-the-art sample average approximations which require impractically large amounts of data in tail probability regions, the proposed approximation scheme exploits the self-similarity of heavy-tailed distributions to extrapolate data from suitable lower quantiles. The resulting approximations are shown to be statistically consistent and are amenable for optimization by means of conventional gradient descent. The approximation is guided by means of a systematic importance-sampling scheme whose asymptotic variance reduction properties are rigorously examined. Numerical experiments demonstrate the superiority of the proposed approximations and the ease of implementation points to the versatility of settings to which the approximation scheme can be applied.

In this paper, we study a portfolio selection problem in which an agent trades a risk-free asset and multiple risky assets with deterministic mean return rates and volatility and wants to maximize the $\alpha$-quantile of her wealth at some terminal time. Because of the time inconsistency caused by quantiles, we consider intra-personal equilibrium strategies. We find that among the class of time-varying, affine portfolio strategies, the intra-personal equilibrium does not exist when $\alpha>1/2$, leads to zero investment in the risky assets when $\alpha<1/2$, and is a portfolio insurance strategy when $\alpha=1/2$. We then compare the intra-personal equilibrium strategy in the case of $\alpha=1/2$, namely under median maximization, to some other strategies and apply it to explain why more wealthy people invest more precentage of wealth in risky assets. Finally, we extend our model to account for multiple terminal time.

In this paper we propose an efficient pricing-hedging framework for volatility derivatives which simultaneously takes into account path roughness and jumps. Instead of dealing with log-volatility, we directly model the instantaneous variance of a risky asset in terms of a fractional Ornstein-Uhlenbeck process driven by an infinite-activity L\'{e}vy subordinator, which is shown to exhibit roughness under suitable conditions and also eludes the need for an independent Brownian component. This structure renders the characteristic function of forward variance obtainable at least in semi-closed form, subject to a generic integrable kernel. To analyze financial derivatives, primarily swaps and European-style options, on average forward volatility, we introduce a general class of power-type derivatives on the average forward variance, which also provide a way of adjusting the option investor's risk exposure. Pricing formulae are based on numerical inverse Fourier transform and, as illustrated by an empirical study on VIX options, permit stable and efficient model calibration once specified.

This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito's lemma, this FPE is associated with a stochastic differential equation (SDE) that models the time evolution of the price return in a fashion different from the classical Black-Scholes equation. Both FPE and SDE equations account for a deterministic part or trend, and a stationary, stochastic part as a q-Gaussian noise. The model is validated using the S\&P500 index's data. After removing the trend from the index, we show that the detrended part is stationary by evaluating the Hurst exponent of the multifractal time series, its power spectrum, and its autocorrelation.

We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while maintaining low probability of blackouts. The key question we investigate are empirical simulation procedures for learning the admissible control set that is specified implicitly through a probability constraint on the system state. We propose a variety of relevant statistical tools including logistic regression, Gaussian process regression, quantile regression and support vector machines, which we then incorporate into an overall Regression Monte Carlo (RMC) framework for approximate dynamic programming. Our results indicate that using logistic or Gaussian process regression to estimate the admissibility probability outperforms the other options. Our algorithms offer an efficient and reliable extension of RMC to probability-constrained control. We illustrate our findings with two case studies for the microgrid problem.

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a return series. The realized EGARCH model is extended by adopting a standardized Student-t and a standardized skewed Student-t distribution for the return equation. Different types of realized measures, such as sub-sampled realized variance, sub-sampled realized range, and realized kernel, are considered in the paper. The Bayesian Markov chain Monte Carlo (MCMC) estimation employs the robust adaptive Metropolis algorithm (RAM) in the burn in period and the standard random walk Metropolis in the sample period. The Bayesian estimators show more favourable results than maximum likelihood estimators in a simulation study. We test the proposed models with several indices to forecast one-step-ahead Value at Risk (VaR) and Expected Shortfall (ES) over a period of 1000 days. Rigorous tail risk forecast evaluations show that the realized EGARCH models employing the standardized skewed Student-t distribution and incorporating sub-sampled realized range are favored, compared to a range of models.