This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Uniform Polynomial Rates of Convergence for A Class of Levy-Driven Controlled SDEs Arising in Multiclass Many-Server Queues.- Nudged Particle Filters in Multiscale Chaotic Systems.- Postponing Collapse: Ergodic Control with a Probabilistic Constraint.- Resource Sharing Networks and Brownian Control Problems.- American Option Model and Negative Fichera Function on Degenerate Boundary.- Continuous-Time Markov Chain and Regime Switching Approximations.- Numerical Approximations for Discounted Continuous Time Markov Decision Processes.- Some Linear-Quadratic Stochastic Dierential Games Driven by State Dependent Gauss-Volterra Processes.- Correlated Equilibria for Infinite Horizon Nonzero-Sum Stochastic Differential Games.- Lattice Dynamical Systems in the Biological Sciences.- Balancing Prevention and Suppression of Forest Fires with Fuel Management as a Stock.- A Free-Model Characterization of the Asymptotic Certainty Equivalent by the Arrow-Pratt Index.- Binary Mean Field Stochastic Games: Stationary Equilibria and Comparative Statics Queues.- Equivalence of Fluid Models for Gt=GI=N + GI Queues.- Stochastic HJB Equations and Regular Singular Points.- Information Diusion in Social Networks: Friendship Paradox based Models and Statistical Inference.- Portfolio Optimization Using Regime-Switching Stochastic Interest Rate and Stochastic Volatility Models.- On Optimal Stopping and Impulse Control with Constraint.- Linear-Quadratic McKean-Vlasov Stochastic Differential Games.- Stochastic Multigroup Epidemic Models: Duration and Final Size.- H2 Dynamic Output Feedback Control for Hidden Markov Jump Linear Systems.- Time-Inconsistent Optimal Control Problems and Related Issues.- Regime-Switching Jump Diusions with Non-Lipschitz Coecients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties.