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European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…

We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…

This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…

We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…

Sponsored search auctions are commonly modeled as an assignment of a fixed set of slots (positions) to a set of advertisers, with welfare maximization being reducible to a standard matching problem. Motivated by modern ad formats, we study…

Consumers often face products sold as lotteries rather than fixed outcomes. A prominent case is the loot box in video games, where players pay for randomized rewards. We investigate how presentation formats shape consumer beliefs and…

The emergence of real-time auction in online advertising has drawn huge attention of modeling the market competition, i.e., bid landscape forecasting. The problem is formulated as to forecast the probability distribution of market price for…

In display advertising, users' online ad experiences are important for the advertising effectiveness. However, users have not been well accommodated in real-time bidding (RTB). This further influences their site visits and perception of the…

Freight brokerages negotiate thousands of carrier rates daily under dynamic pricing conditions where models frequently revise targets mid-conversation. Classical time-dependent concession frameworks use a fixed shape parameter $\beta$ that…

This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is…

Online advertising is progressively moving towards a programmatic model in which ads are matched to actual interests of individuals collected as they browse the web. Letting the huge debate around privacy aside, a very important question in…

The implied volatility smile surface is the basis of option pricing, and the dynamic evolution of the option volatility smile surface is difficult to predict. In this paper, attention mechanism is introduced into LSTM, and a volatility…

The auction theory literature has so far focused mostly on the design of mechanisms that takes the revenue or the efficiency as a yardstick. However, scenarios where the {\it capacity}, which we define as \textit{``the number of bidders the…

Online bidding and auction are crucial aspects of the online advertising industry. Conventionally, there is only one slot for ad display and most current studies focus on it. Nowadays, multi-slot display advertising is gradually becoming…

This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and…

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally…

Online advertising and product recommendation are important domains of applications for multi-armed bandit methods. In these fields, the reward that is immediately available is most often only a proxy for the actual outcome of interest,…

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…

We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety…

In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can…