Model-Free Reinforcement Learning has achieved meaningful results in stable environments but, to this day, it remains problematic in regime changing environments like financial markets. In contrast, model-based RL is able to capture some fundamental and dynamical concepts of the environment but suffer from cognitive bias. In this work, we propose to combine the best of the two techniques by selecting various model-based approaches thanks to Model-Free Deep Reinforcement Learning. Using not only past performance and volatility, we include additional contextual information such as macro and risk appetite signals to account for implicit regime changes. We also adapt traditional RL methods to real-life situations by considering only past data for the training sets. Hence, we cannot use future information in our training data set as implied by K-fold cross validation. Building on traditional statistical methods, we use the traditional "walk-forward analysis", which is defined by successive training and testing based on expanding periods, to assert the robustness of the resulting agent.

Finally, we present the concept of statistical difference's significance based on a two-tailed T-test, to highlight the ways in which our models differ from more traditional ones. Our experimental results show that our approach outperforms traditional financial baseline portfolio models such as the Markowitz model in almost all evaluation metrics commonly used in financial mathematics, namely net performance, Sharpe and Sortino ratios, maximum drawdown, maximum drawdown over volatility.

Financial literacy and financial education are important components of modern life. The importance of financial literacy is increasing for financial consumers because of the weakening of both government and employer-based retirement systems. Unfortunately, empirical research shows that financial consumers are not fully informed and are not able to make proper choices even when appropriate information is available. More research is needed as to how financial consumers obtain investment and financial planning information. A primary data study was conducted to understand the differences between the demographic categories of gender, age, education-level, and income-level with the means of obtaining investment and financial planning information. In this research study, which selected a population from the LinkedIn platform, statistical differences between gender, age, education-level, and income-level were confirmed. These differences helped to confirm prior research in this field of study. Practical opportunities for commercial outreach to specific populations became evident through this type of research. Providers of investment and financial planning information can access their targeted audience more effectively by understanding the demographic profile of the audience, as well as the propensity of the demographic profile of the audience to respond. As this type of research is relatively easy to construct and administer, commercial outreach for providers of investment and financial planning information can be conducted in a cost-efficient and effective manner.

For the Barndorff-Nielsen and Shephard model, we present approximate expressions of call option prices based on the decomposition formula developed by Arai (2021). Besides, some numerical experiments are also implemented to make sure how effective our approximations are.

Public transport ridership around the world has been hit hard by the COVID-19 pandemic. Travellers are likely to adapt their behaviour to avoid the risk of transmission and these changes may even be sustained after the pandemic. To evaluate travellers' behaviour in public transport networks during these times and assess how they will respond to future changes in the pandemic, we conduct a stated choice experiment with train travellers in the Netherlands. We specifically assess behaviour related to three criteria affecting the risk of COVID-19 transmission: (i) crowding, (ii) exposure duration, and (iii) prevalent infection rate.

Observed choices are analysed using a latent class choice model which reveals two, nearly equally sized traveller segments: 'COVID Conscious' and 'Infection Indifferent'. The former has a significantly higher valuation of crowding, accepting, on average 8.75 minutes extra waiting time to reduce one person on-board. Moreover, they demonstrate a strong desire to sit without anybody in their neighbouring seat and are quite sensitive to changes in the prevalent infection rate. By contrast, Infection Indifferent travellers' value of crowding (1.04 waiting time minutes/person) is only slightly higher than pre-pandemic estimates and they are relatively unaffected by infection rates. We find that older and female travellers are more likely to be COVD Conscious while those reporting to use the trains more frequently during the pandemic tend to be Infection Indifferent. Further analysis also reveals differences between the two segments in attitudes towards the pandemic and self-reported rule-following behaviour. The behavioural insights from this study will not only contribute to better demand forecasting for service planning but will also inform public transport policy decisions aimed at curbing the shift to private modes.

We consider identification of peer effects under peer group miss-specification. Our model of group miss-specification allows for missing data and peer group uncertainty. Missing data can take the form of some individuals being completely absent from the data, and the researcher need not have any information on these individuals and may not even know that they are missing. We show that peer effects are nevertheless identifiable if these individuals are missing completely at random, and propose a GMM estimator which jointly estimates the sampling probability and peer effects. In practice this means that the researcher need only have access to an individual/household level sample with group identifiers. The researcher may also be uncertain as to what is the relevant peer group for the outcome under study. We show that peer effects are nevertheless identifiable provided that the candidate peer groups are nested within one another (e.g. classroom, grade, school) and propose a non-linear least squares estimator. We conduct a Monte-Carlo experiment to demonstrate our identification results and the performance of the proposed estimators in a setting tailored to real data (the Dartmouth room-mate data).

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the theory of set-valued maps. In particular, using results from Beiglb\"ock, Jourdain, Margheriti, and Pammer [5], we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals. Moreover, we establish compactness of the set of optimizers as well as upper hemicontinuity of the optimizers w.r.t. the marginals.

We introduce the price probability measure {\eta}(p;t) that defines the mean price p(1;t), mean square price p(2;t), price volatility {\sigma}p2(t)and all price n-th statistical moments p(n;t) as ratio of sums of n-th degree values C(n;t) and volumes U(n;t) of market trades aggregated during certain time interval {\Delta}. The definition of the mean price p(1;t) coincides with definition of the volume weighted average price (VWAP) introduced at least 30 years ago. We show that price volatility {\sigma}p2(t) forecasting requires modeling evolution of the sums of second-degree values C(2;t) and volumes U(2;t). We call this model as second-order economic theory. We use numerical continuous risk ratings as ground for risk assessment of economic agents and distribute agents by risk ratings as coordinates. We introduce continuous economic media approximation of squares of values and volumes of agents trades and their flows aggregated during time interval {\Delta}. We take into account expectations that govern agents trades and introduce aggregated expectations alike to aggregated trades. We derive equations for continuous economic media approximation on the second-degree trades. In the linear approximation we derive mean square price p(2;t) and volatility {\sigma}p2(t) disturbances as functions of the first and second-degree trades disturbances. Description of each next n-th price statistical moment p(n;t) with respect to the unit price measure {\eta}(p;t) depends on sums of n-th degree values C(n;t) and volumes U(n;t) of market trades and hence requires development of the corresponding n-th order economic theory.