Dynamic Programming (DP) avoiding the proof of the Dynamic Programming Principle (DPP):

a)  using  Perron's method and some possible offshoots in continuous-time stochastic control and games

1.  Optimal investement with high-watermark fee
    2.  Stochastic Perron Method for control problems or static games of optimal stopping
    3.  (Dynamic) Zero-sum games over feed-back strategies and Stochastic Perron
    4. Asymptotic Perron's method and Markov controls/strategies

b) Transaction costs: the shadow price approach and well posed-ness

(it fits under the umbrella of "DP avoiding the DPP"):

Some old slides on unpublished work on risk-tolerance wealth processes for exponential-like utility