{"id":49,"date":"2021-02-23T10:40:34","date_gmt":"2021-02-23T15:40:34","guid":{"rendered":"http:\/\/pages.charlotte.edu\/jpbishwa\/?page_id=49"},"modified":"2021-03-17T14:06:40","modified_gmt":"2021-03-17T18:06:40","slug":"research-interests","status":"publish","type":"page","link":"https:\/\/pages.charlotte.edu\/jpbishwa\/research-interests\/","title":{"rendered":"Research Interests"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Stochastic Differential Inference (SDI)<\/h2>\n\n\n\n

Models<\/h3>\n\n\n\n
  • Discretely Observed Diffusions<\/li>
  • Stochastic Differential Equations<\/li>
  • Semimartingales and Levy driven SDEs<\/li>
  • SDEs driven by Fractional Brownian Motion<\/li>
  • Stochastic Filtering and Stochastic Volatility Models<\/li>
  • Anticipative Stochastic Differential Equations<\/li>
  • Stochastic Partial Differential Equations<\/li>
  • Stochastic Navier-Stokes Equation, KPZ Equation<\/li>
  • Interacting Particle Systems, Superdiffusions<\/li><\/ul>\n\n\n\n

    Methods<\/h3>\n\n\n\n
    • Higher-Order Asymptotics<\/li>
    • Sequential Methods<\/li>
    • Monte Carlo Methods<\/li>
    • Particle Filters
      (Sequential Monte Carlo)<\/li>
    • Bayesian Methods<\/li>
    • Nonparametric Methods<\/li>
    • Semiparametric Methods<\/li>
    • Sieve Methods<\/li>
    • Bootstrap Methods<\/li>
    • Robust Methods<\/li>
    • Asymptotic Equivalence<\/li>
    • Hypothesis Testing<\/li><\/ul>\n\n\n\n

      Mathematical Finance and Financial Econometrics<\/h2>\n\n\n\n
      • Computational Finance<\/li>
      • Term Structure of Interest Rates<\/li>
      • Asset Pricing, Options Pricing and Hedging<\/li>
      • Fractional Brownian Motion in Finance<\/li>
      • Lattice Methods for Derivatives Pricing<\/li>
      • Weak Convergence of Financial Markets<\/li>
      • Real Options in Corporate Finance<\/li>
      • Risk Management and Insurance<\/li>
      • Valuation and Estimation of Credit Risk<\/li>
      • Extreme Value Theory<\/li>
      • Incomplete Markets<\/li>
      • High-Frequency Data<\/li>
      • Market Microstructure<\/li>
      • Stochastic Volatility<\/li>
      • Hawkes Process in Finance<\/li><\/ul>\n\n\n\n

        Stochastic Analysis and Probability<\/h2>\n\n\n\n
        • Diffusions in Random Environments<\/li>
        • Berry-Esseen Theorems and Large Deviations<\/li>
        • Stochastic Numerical Analysis<\/li>
        • Fractional Stochastic Calculus<\/li>
        • Malliavin Calculus<\/li>
        • Anticipative Stochastic Calculus<\/li><\/ul>\n\n\n\n

          Mathematical Biology<\/h2>\n\n\n\n
          • Nonlinear SPDE in Neurobiology<\/li>
          • Gomperz Diffusion Models for Tumor Growth<\/li>
          • Sub-diffusion Models for Nanoscale Biophysics<\/li>
          • SPDE with Jumps for Neurons<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"

            Stochastic Differential Inference (SDI) Models Discretely Observed Diffusions Stochastic Differential Equations Semimartingales and Levy driven SDEs SDEs driven by Fractional Brownian Motion Stochastic Filtering and Stochastic Volatility Models Anticipative Stochastic Differential Equations Stochastic Partial Differential Equations Stochastic Navier-Stokes Equation, KPZ Equation Interacting Particle Systems, Superdiffusions Methods Higher-Order Asymptotics Sequential Methods Monte Carlo Methods Particle Filters(Sequential […]<\/p>\n","protected":false},"author":13,"featured_media":0,"parent":0,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-49","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/pages\/49","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/comments?post=49"}],"version-history":[{"count":6,"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/pages\/49\/revisions"}],"predecessor-version":[{"id":230,"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/pages\/49\/revisions\/230"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/jpbishwa\/wp-json\/wp\/v2\/media?parent=49"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}