Culp’s Hill: Key to Union Success at Gettysburg

Brigadier General George S. Greene’s position on Culp’s Hill during the Battle of Gettysburg is arguably the crucial lynchpin of July 2, 1863. Had this position at the barb of the fishhook defensive line fallen, Confederate General Robert E. Lee and his army would then have been positioned to take Cemetery Hill, thus breaking the curve of the hook on the Union right. This most likely would have sent the Union into retreat, leaving the direct route to Washington unguarded. Fortunately, valiant efforts were made by men like Generals George S. Greene and Henry H. Lockwood in order to preserve the Union Army’s possession of the hill and, as a result, preserve the Union itself. While leaders distinguished themselves during the Battle of Gettysburg with exceptional decision-making and ingenuity, the battle for Culp’s Hill also embodied the personal cost these decisions made, as evidenced by the experience of Marylanders who literally fought their neighbors. [excerpt

Exploratory Control with Tsallis Entropy for Latent Factor Models

We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis Entropy and derive the optimal distribution over states - which we prove is $q$-Gaussian distributed with location characterized through the solution of an FBS$\Delta$E and FBSDE in discrete and continuous time, respectively. We discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution. Finally, we develop the optimal policy in a model-agnostic setting along the lines of soft $Q$-learning. The approach may be applied in, e.g., developing more robust statistical arbitrage trading strategies

Exploratory Control with Tsallis Entropy for Latent Factor Models

We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis entropy and derive the optimal distribution over states—which we prove is q-Gaussian distributed with location characterized through the solution of an BSΔE and BSDE in discrete and continuous time, respectively. We discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution. Finally, we develop the optimal policy in a model-agnostic setting along the lines of soft Q-learning. The approach may be applied in, e.g., developing more robust statistical arbitrage trading strategies

Optimal Trading with Differing Trade Signals

We consider the problem of maximizing portfolio value when an agent has a subjective view on asset value which differs from the traded market price. The agent's trades will have a price impact which affect the price at which the asset is traded. In addition to the agent's trades affecting the market price, the agent may change his view on the asset's value if its difference from the market price persists. We also consider a situation of several agents interacting and trading simultaneously when they have a subjective view on the asset value. Two cases of the subjective views of agents are considered, one in which they all share the same information, and one in which they all have an individual signal correlated with price innovations. To study the large agent problem we take a mean-field game approach which remains tractable. After classifying the mean-field equilibrium we compute the cross-sectional distribution of agents' inventories and the dependence of price distribution on the amount of shared information among the agents

Optimal Decisions in a Time Priority Queue

Elementary Schoolhttps://egrove.olemiss.edu/phay_jon/1633/thumbnail.jp

Insider trading with temporary price impact

We model an informed agent with information about the future value of an asset trying to maximize profits when the agent's trades are subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model, equilibrium is characterized by the unique root of a particular polynomial. Analysis of this polynomial with small levels of risk-Aversion and transaction costs reveal a dimensionless parameter which captures several orders of asymptotic accuracy of the equilibrium behavior. In a continuous time analogue of the single auction model, incorporation of a transaction costs allows the informed agent's optimal trading strategy to be obtained in feedback form. Linear equilibrium is characterized by the unique solution to a system of two ordinary differential equations, of which one is forward in time and one is backward. When transaction costs are in effect, the price set by the market maker in equilibrium is not fully revealing of the informed agent's private signal, leaving an information gap at the end of the trading interval. When considering vanishing transaction costs, the equilibrium trading strategy and pricing rules converge to their frictionless counterparts. </p

Hedging Non-Tradable Risks with Transaction Costs and Price Impact

A risk-averse agent hedges her exposure to a non-tradable risk factor $U$ using a correlated traded asset $S$ and accounts for the impact of her trades on both factors. The effect of the agent's trades on $U$ is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in $U$. When the exposure to the non-tradable risk factor $\psi(U_T)$ is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when $\psi(U_T)$ is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.Comment: Originally posted to SSRN April 27, 2018. Forthcoming in Mathematical Financ

Staying Civil: Conscientious Objection and Civil Society in West Germany, 1956-1966

In the years following WWII, the West German peace movement emerged from its dormancy, developed into a popular movement, rose to challenge the policy of the government, and changed the character of West German society. The development of peace activism in postwar West Germany was a process that required the efforts of people willing to push the boundaries of the normal spheres of political life. The training ground for many of these peace activists was the West German conscientious objection (CO) movement. By studying their learning process as they rediscovered pacifist traditions as well as the organizations and the transnational networks they cultivated, we can learn a great deal about the foundations of the protest movements of the late 1960s. This dissertation examines the origins and activities of the early West German CO protest groups and problematizes the role of these groups in the early West German peace movement. The groups were an integral part of the broader German peace movement and frequently participated in peace demonstrations both nationally and internationally. The organizational development of the CO groups in the 1950s and early 1960s laid the groundwork for the emergence of larger and more popular protest movements that played major roles in the turbulent late 1960s. The individual actors who were the catalysts of change and growth for the conscientious objection movement and the peace movement as a whole are an essential element of my dissertation. The contacts they made, the relationships they developed, the philosophical teachings they (re-)discovered, and the protest culture they cultivated are fundamental to understanding how the peace movement left its mark on West German society. Often dismissed as a ‘single issue’ campaign, I argue that although CO groups primarily focused on conscientious objection, they also promoted a complex set of issues regarding political legitimacy, the role of the postwar state, and challenged the right of an older generation over the use of their bodies. My work challenges the traditional understanding of the conscientious objection movement in West Germany and elucidates the early development of extra-parliamentary opposition