We consider the Bachelier model with information delay where investment decisions can be based only on observations from $H>0$ time units before. Utility indifference prices are studied for vanilla options and we compute their non-trivial scaling limit for vanishing delay when risk aversion is scaled liked $A/H$ for some constant $A$. Using techniques from [7], we develop discrete-time duality for this setting and show how the relaxed form of martingale property introduced by [9] results in the scaling limit taking the form of a volatility control problem with quadratic penalty.

We implement and test kernel averaging Non-Uniform Fast Fourier Transform (NUFFT) methods to enhance the performance of correlation and covariance estimation on asynchronously sampled event-data using the Malliavin-Mancino Fourier estimator. The methods are benchmarked for Dirichlet and Fej\'{e}r Fourier basis kernels. We consider test cases formed from Geometric Brownian motions to replicate synchronous and asynchronous data for benchmarking purposes. We consider three standard averaging kernels to convolve the event-data for synchronisation via over-sampling for use with the Fast Fourier Transform (FFT): the Gaussian kernel, the Kaiser-Bessel kernel, and the exponential of semi-circle kernel. First, this allows us to demonstrate the performance of the estimator with different combinations of basis kernels and averaging kernels. Second, we investigate and compare the impact of the averaging scales explicit in each averaging kernel and its relationship between the time-scale averaging implicit in the Malliavin-Mancino estimator. Third, we demonstrate the relationship between time-scale averaging based on the number of Fourier coefficients used in the estimator to a theoretical model of the Epps effect. We briefly demonstrate the methods on Trade-and-Quote (TAQ) data from the Johannesburg Stock Exchange to make an initial visualisation of the correlation dynamics for various time-scales under market microstructure.

The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock price crash due to the investors' rapid and synchronous sell-off. However, within a short period, the quality sectors start recovering from the bottom. A stock price model has been developed during such crises based on the net-fund-flow ($\Psi_t$) due to institutional investors, and financial antifragility ($\phi$) of a company. We assume that during the crash, the stock price fall is independent of the $\phi$. We study the effects of shock lengths and $\phi$ on the stock price during the crises period using the $\Psi_t$ obtained from synthetic and real fund flow data. We observed that the possibility of recovery of stock with $\phi>0$, termed as quality stock, decreases with an increase in shock-length beyond a specific period. A quality stock with higher $\phi$ shows V-shape recovery and outperform others. The shock length and recovery period of quality stock are almost equal that is seen in the Indian market. Financially stressed stocks, i.e., the stocks with $\phi<0$, show L-shape recovery during the pandemic. The stock data and model analysis shows that the investors, in uncertainty like COVID-19, invest in quality stocks to restructure their portfolio to reduce the risk. The study may help the investors to make the right investment decision during a crisis.

In this paper we propose a new methodology for solving a discrete time stochastic Markovian control problem under model uncertainty. By utilizing the Dirichlet process, we model the unknown distribution of the underlying stochastic process as a random probability measure and achieve online learning in a Bayesian manner. Our approach integrates optimizing and dynamic learning. When dealing with model uncertainty, the nonparametric framework allows us to avoid model misspecification that usually occurs in other classical control methods. Then, we develop a numerical algorithm to handle the infinitely dimensional state space in this setup and utilizes Gaussian process surrogates to obtain a functional representation of the value function in the Bellman recursion. We also build separate surrogates for optimal control to eliminate repeated optimizations on out-of-sample paths and bring computational speed-ups. Finally, we demonstrate the financial advantages of the nonparametric Bayesian framework compared to parametric approaches such as strong robust and time consistent adaptive.

Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows us to convert an optimization of a non-convex distortion riskmetric with distributional uncertainty to a convex one, leading to great tractability. The key to the unifying equivalence result is the novel notion of closedness under concentration of sets of distributions. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, Value-at-Risk, Expected Shortfall, and Yaari's dual utility under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.

This paper extends the work of Boudt and Pertitjean(2014) and investigates the trading patterns before price jumps in the stock market based on a new multivariate time classification technique. Different from Boudt and Pertitjean(2014), our analyzing scheme can explore the "time-series information" embedded in the trading-related attributes and provides a set of jump indicators for abnormal pattern recognition. In addition to the commonly used liquidity measures, our analysis also involves a set of technical indicators to describe the micro-trading behaviors. An empirical study is conducted on the level-2 data of the constituent stocks of China Security Index 300. It is found that among all the candidate attributes, several volume and volatility-related attributes exhibit the most significant abnormality before price jumps. Though some of the abnormalities start just shortly before the occurrence of the jumps, some start much earlier. We also find that most of our attributes have low mutual dependencies with each other from the perspective of time-series analysis, which allows various perspectives to study the market trading behaviors. To this end, our experiment provides a set of jump indicators that can effectively detect the stocks with extremely abnormal trading behaviors before price jumps. More importantly, our study offers a new framework and potential useful directions for trading-related pattern recognition problem using the time series classification techniques.

We analyze the phenomena of spontaneous symmetry breaking in Quantum Finance by using as a starting point the Black-Scholes (BS) and the Merton-Garman (MG) equations expressed in the Hamiltonian form. In this scenario the martingale condition (state) corresponds to the vacuum state which becomes degenerate when the symmetry of the system is spontaneously broken. We then analyze the broken symmetries of the system and we interpret from the perspective of Financial markets the possible appearance of the Nambu-Goldstone bosons.

How do you value companies which have IPOed recently? How do you compare them amongst their peers? Valuing companies using a linear extrapolation of their revenues and profits leads to an ingenious method to benchmark stocks against each other. Here we present such a method, dubbed the growth average U1.

In this paper we devise a statistical method for tracking and modeling change-points on the dependence structure of multivariate extremes. The methods are motivated by and illustrated on a case study on crypto-assets.